Kinds Of Function ( Reflexive, Symmetric , Transitive Antisymmetric ) By Ishrat Hayat Malik

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">Kinds Of Function ( Reflexive, Symmetric , Transitive Antisymmetric ) By Ishrat Hayat Malik</span></h2> <div> <span style="background-color: cyan;"></span><br /> <h3 style="text-align: left;"> <span style="background-color: cyan;"> <b><u>Kinds Of Function In Discrete Structure<div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji0wFKx__ntFlL_U8BJ_hoim-TlIDAuqhLpSXnYwB2QmeD5WYMC7a5bk-X3PwJ4kdqrGFpyMa2liaxCp8gq1ePxClXGMXBZytIWD_cyTuHlDVweP5Lu9pr4U0bXtzKCLPvBeEqubef5cFy/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji0wFKx__ntFlL_U8BJ_hoim-TlIDAuqhLpSXnYwB2QmeD5WYMC7a5bk-X3PwJ4kdqrGFpyMa2liaxCp8gq1ePxClXGMXBZytIWD_cyTuHlDVweP5Lu9pr4U0bXtzKCLPvBeEqubef5cFy/s320/slide_1.jpg" width="320" /></a></div> </u></b></span></h3> <span style="background-color: cyan;"> </span> <h3 style="text-align: left;"> <span style="background-color: cyan;"> <span style="font-weight: normal;">1) Reflexive<br />2) Symmetric<br />3) Transitive<br />4) Anti-Symmetric</span></span></h3> <span style="background-color: cyan;"> </span><span style="background-color: cyan;"><h3 style="text-align: left;"> <b><u>• Reflexive:</u></b> The relation R on {1,2,3} given by</h3> <h3 style="text-align: left;"> <span style="font-weight: normal;">R = {(1,1), (2,2), (2,3), (3,3)} is reflexive. (All<br />loops are present.)</span></h3> <h3 style="text-align: left;"> <b><u>• Symmetric</u></b>: The relation R on {1,2,3} given by</h3> <h3 style="text-align: left;"> <span style="font-weight: normal;">R = {(1,1), (1,2), (2,1), (1,3), (3,1)} is symmetric.<br />(All paths are 2-way.)</span></h3> <h3 style="text-align: left;"> •<b><u> Transitive:</u></b> The relation R on {1,2,3} given by</h3> <h3> <span style="font-weight: normal;">R = {(1,1), (1,2), (2,1), (2,2), (2,3), (1,3)} is<br />transitive. (If I can get from one point to another<br />in 2 steps, then I can get there in 1 step.)</span></h3> <h3 style="text-align: left;"> <b><u>Anti-Symmetric</u></b>  </h3> <h3 style="text-align: left;"> <span style="font-weight: normal;">R = {(1,1), (1,2), (3,2), (3,3)} is antisymmetric. • Is every relation symmetric or anti-symmetric? • No! Consider R = {(1,2), (2,1), (1,3)}</span></h3> <div> <h3 style="text-align: center;"> <u style="font-weight: normal;">Violations of the Properties</u></h3> <h3 style="text-align: left;"> <span style="font-weight: normal;">• Why is R = {(1,1), (2,2), (3,3)} not reflexive on<br />{1,2,3,4}?<br />Because (4,4) is missing.<br />• Why is R = {(1,2), (2,1), (3,1)} not symmetric?<br />Because (1,3) is missing.<br />• Why is R = {(1,2), (2,3), (1,3), (2,1)} not<br />transitive?<br />Because (1,1) and (2,2) are missing.<br />• Is {(1,1), (2,2), (3,3)} symmetric? transitive?<br /> Yes! Yes!</span></h3> </div> <div> <br /></div> </span><span style="background-color: cyan;"><div style="font-weight: normal;"> <br /></div> </span></div> </div>

Kinds Of Function ( Reflexive, Symmetric , Transitive Antisymmetric ) By Ishrat Hayat Malik

Kinds Of Function ( Reflexive, Symmetric , Transitive Antisymmetric ) By Ishrat Hayat Malik Kinds Of Function In Discrete Structure ...

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How to print the leap years of 20th centuries in for Loop c++ By Munavar Ahmad

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">How to print the leap years of 20th centuries in for Loop c++ By Munavar Ahmad</span></h2> <div> <span style="background-color: cyan;"></span><br /> <div> <span style="background-color: cyan;">#include<iostream></span></div> <span style="background-color: cyan;"> <div> using namespace std;<br /> <div style="text-align: right;"> </div> </div> <div> int main()<br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s200/slide_1.jpg" width="200" /></a></div> </div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int i;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>for(i=1901;i<=2000;i++)</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>{</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>if(i%4==0)</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<i<<endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div> }</div> <div style="font-weight: normal;"> <br /></div> </span></div> </div>

How to print the leap years of 20th centuries in for Loop c++ By Munavar Ahmad

How to print the leap years of 20th centuries in for Loop c++ By Munavar Ahmad #include<iostream> using namespace std; i...

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How to print the sum of a Number of 4 digit for loop c++ By Munavar Ahmad

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">How to print the sum of a Number of 4 digit  for loop c++ By Munavar Ahmad</span></h2> <div> <span style="background-color: cyan;"></span><br /> <div> <span style="background-color: cyan;">#include<iostream></span></div> <span style="background-color: cyan;"> <div> using namespace std;</div> <div> int main()<br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s200/slide_1.jpg" width="200" /></a></div> </div> <div> {</div> <div> int num,a,b,c,d,e,f,sum;</div> <div> cout<<"Enter A number of 4 digits";</div> <div> cin>>num;</div> <div> a=num%10;</div> <div> b=num/10;</div> <div> c=b%10;</div> <div> d=b/10;</div> <div> e=d%10;</div> <div> f=d/10;</div> <div> sum=a+c+e+f;</div> <div> cout<<"The Sum Of Digits is"<<" "<<sum;</div> <div> return 0;</div> <div> }</div> </span></div> </div>

How to print the sum of a Number of 4 digit for loop c++ By Munavar Ahmad

How to print the sum of a Number of 4 digit  for loop c++ By Munavar Ahmad #include<iostream> using namespace std; int main...

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How to print the series 1 3 5 9 17 33 For Loop C++ By Manavar Ahmad

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">How to print the series 1 3  5 9 17 33 For Loop C++ By Manavar Ahmad</span></h2> <div> <span style="background-color: cyan;"></span><br /> <div> <span style="background-color: cyan;">#include<iostream></span></div> <span style="background-color: cyan;"> </span> <div> <span style="background-color: cyan;">using namespace std;</span><br /> <div class="separator" style="clear: both; text-align: center;"> <span style="background-color: cyan;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmCFWNOW2-05M7MYkkItNQbXG_yOrVM_8Y6cKMje6A6PJivOCDgkjzGI4Fv_ea1He3BQ8AUwqOWgYTRxwj-voBxjTpGcrfRcxnguRaxYRspjclGSHTLBnicrZXFwHTmadWp6er7bpaP69K/s200/slide_1.jpg" width="200" /></a></span></div> </div> <span style="background-color: cyan;"> <div> int main()</div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int i;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>for(i=3;i<=33;i=i*2-1)</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>{</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<i<<" ";</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div> }</div> </span></div> </div>

How to print the series 1 3 5 9 17 33 For Loop C++ By Manavar Ahmad

How to print the series 1 3  5 9 17 33 For Loop C++ By Manavar Ahmad #include<iostream> using namespace std; int main(...

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How to print 1 3 6 10 15 21 in c++ By Sir Munavar Ahmad

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: left;"> <span style="background-color: cyan; font-weight: normal;">How to print 1 3 6 10 15 21 in c++ By Sir Munavar Ahmad</span></h2> <div> <span style="background-color: cyan;"></span><br /> <div style="text-align: left;"> <span style="background-color: cyan;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9m2fi2VjQtQu-EHDy3kbU-rT89sFKfYzHKbP1-lmtQt6q_IgQUbyb2LAQLIGQUgA1iWiA8l4NBpLOTmWXGbxnIjJdSsyGg1KJL1STazo60gv8nDSSOXU9m9MKZvzUFrUtY5aomSjBwA15/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9m2fi2VjQtQu-EHDy3kbU-rT89sFKfYzHKbP1-lmtQt6q_IgQUbyb2LAQLIGQUgA1iWiA8l4NBpLOTmWXGbxnIjJdSsyGg1KJL1STazo60gv8nDSSOXU9m9MKZvzUFrUtY5aomSjBwA15/s200/slide_1.jpg" width="200" /></a>#include<iostream></span></div> <span style="background-color: cyan;"> <div style="text-align: left;"> using namespace std;</div> <div style="text-align: left;"> int main()</div> <div style="text-align: left;"> {</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>int i,inc;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>inc=2;</div> <div style="text-align: left;"> for(i=1;i<=21;i=i+inc++)</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>{</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<i<<" ";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div style="text-align: left;"> }</div> </span></div> </div>

How to print 1 3 6 10 15 21 in c++ By Sir Munavar Ahmad

How to print 1 3 6 10 15 21 in c++ By Sir Munavar Ahmad #include<iostream> using namespace std; int main() { int i,inc...

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Good Listening and Bad Listening & Purpose Of Listening & Pitfalls Of Listening (Bussiness Communication) Mam Najiba

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;"><u>Purpose Of Listening (Bussiness Communication) Mam Najiba</u></span></h2> <div> <div> <span style="background-color: white;"><b>Listening</b> is an important aspect of business communication. It stands third after writing</span></div> <div> <span style="background-color: white;">and speaking. A business communicator has to listen to various customer, employees, officer,</span></div> <div> <span style="background-color: white;">suppliers, financiers etc. Obviously, it is an unavoidable task for a business person. This important</span></div> <div> <span style="background-color: white;">reason as to why a business communicator should known about listening is enumerated as under.</span></div> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">(1) To gain new information and ideas.<br />(2) To question and test evidence and assumptions.<br />(3) To be inspired and motivated.<br />(4) To improve overall communication.</span></h3> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh77KeP94y9e6bIlSgwL5zIWxZODWoIegdHhfCFp6rxcwpac9euXhpPZY4QnoyOyPfy1yboaqKpthjJKtfK6uqGgRFARiWO_mB_f-7rt7Auubc4ANEmoCcJ244QGC9VyzxlD6S5JXl46qBr/s1600/bbc853fd-133d-42f9-954c-3b9aa3af2df4image1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh77KeP94y9e6bIlSgwL5zIWxZODWoIegdHhfCFp6rxcwpac9euXhpPZY4QnoyOyPfy1yboaqKpthjJKtfK6uqGgRFARiWO_mB_f-7rt7Auubc4ANEmoCcJ244QGC9VyzxlD6S5JXl46qBr/s320/bbc853fd-133d-42f9-954c-3b9aa3af2df4image1.png" width="320" /></a></div> <div> <span style="background-color: white; font-weight: normal;"><br /></span></div> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;"><u>Good Listening and Bad Listening </u></span></h2> <div> <div style="text-align: center;"> <b><u>Good Listening</u></b> : Good listening means a person’s ability to understand the message effectively and efficiently. It results in improved communication and quick feedback.</div> <div> <span style="background-color: white;">Advantage: </span></div> <h3 style="text-align: left;"> <span style="background-color: white;">1.<span class="Apple-tab-span" style="white-space: pre;"> </span> <span style="font-weight: normal;">  It leads to helpful positive attitudes.</span></span><span style="font-weight: normal;"><span style="background-color: white;">2.<span class="Apple-tab-span" style="white-space: pre;"> </span> . It permits the speaker and listener to improve communication.</span><span style="background-color: white;">3.<span class="Apple-tab-span" style="white-space: pre;"> </span> . It provides a feed-back to the speaker who can adjust to the situation and helps              his/her give better presentation. </span><span style="background-color: white;">4.<span class="Apple-tab-span" style="white-space: pre;"> </span>.  It creates better understanding of the two parties.</span></span></h3> <div> <span style="background-color: white;"><b><u>Bad listening:</u></b>- It means a person’s disability to understand the message partially or completely. It results in </span></div> <h3 style="text-align: left;"> <span style="font-weight: normal;"><span style="background-color: white;">(i)<span class="Apple-tab-span" style="white-space: pre;"> </span>Poor hearing</span><span style="background-color: white;">(ii)<span class="Apple-tab-span" style="white-space: pre;"> </span>Poor understanding </span><span style="background-color: white;">(iii)<span class="Apple-tab-span" style="white-space: pre;"> </span>Poor interpretation, </span></span></h3> <div> <span style="background-color: white;">It can be overcome by following the guidelines of listening.</span></div> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;"><u>pitfalls of listening</u></span></h2> </div> <div style="text-align: center;"> <div> Listening is a very important aspect of oral communication. If there is any lacking or fault in listening, it might cause failure to communication process. So, people should be well aware of faults in listening so as to improve the overall communication ability</div> <h3 style="background-color: white; text-align: left;"> <span style="font-weight: normal;">(1) Prejudice against the speaker.<br />(2) External Distraction.<br />(3) Thinking speed.<br />(4) Premature evaluation.<br />(5) Semantic stereotype.</span></h3> <div style="background-color: white;"> <br /></div> </div> <div style="background-color: cyan; font-weight: normal; text-align: center;"> <br /></div> </div> </div>

Good Listening and Bad Listening & Purpose Of Listening & Pitfalls Of Listening (Bussiness Communication) Mam Najiba

Purpose Of Listening (Bussiness Communication) Mam Najiba Listening is an important aspect of business communication. It stands third ...

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Structure Report (Technical and Bussiness Writing) Mam Najiba

<div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">Structure Report ( Bussiness Writing) Mam Najiba</span></h2> <h2 style="text-align: left;"> </h2> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">1) Title Page → Subject matter</span></h3> <h3 style="text-align: left;"> <span style="font-weight: normal;">2) Acknowlegdement → who help you receiving and collecting Data<div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeOaRtINIhzPbllN7K3lcJIFh_VfuQWxlh50qpAxwqm9xjOJbaRoFfky8n0gn-koKDzHjceA4ZbUsLRi78a7rtu0mJ03IbRJOr4JJCeHzoe_JibOeSR5NsNOlUzbbTFFLYFhaMqGvBzcQp/s1600/report.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeOaRtINIhzPbllN7K3lcJIFh_VfuQWxlh50qpAxwqm9xjOJbaRoFfky8n0gn-koKDzHjceA4ZbUsLRi78a7rtu0mJ03IbRJOr4JJCeHzoe_JibOeSR5NsNOlUzbbTFFLYFhaMqGvBzcQp/s320/report.jpg" width="157" /></a></div> </span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">3) Content → Main section with page number Number</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">4) Abstruct Summay → main task used</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">5) Introduction → Object clear define outline</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">6) Methedology → what Form of report question,result,table,grapgh</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">7) Resultant Finding → any more advantage and finding</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">8) Discussion→ Explanation suggestion</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">9) Conclusion → main issue new adittion</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">10) Reference → Other auther name,Data Of Publication, Title Of Book,Page Number</span></h3> <h3 style="text-align: left;"> <span style="background-color: white; font-weight: normal;">11) Appendices → Additional Information,Glossary</span></h3> </div>

Structure Report (Technical and Bussiness Writing) Mam Najiba

Structure Report ( Bussiness Writing) Mam Najiba 1) Title Page → Subject matter 2) Acknowlegdement → who help you receiving and coll...

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Induction In Discrete Structure By Ishrat Hayat Malik

<div dir="ltr" style="text-align: left;" trbidi="on"> <div dir="ltr" style="text-align: left;" trbidi="on"> <h2 style="text-align: center;"> <span style="background-color: cyan; font-weight: normal;">Induction In Discrete Structure By (Ishrat Hayat Malik)</span></h2> <div> <span style="background-color: white;"><b>Define</b></span><span style="background-color: white; font-weight: normal;">: </span> Induction is a mathematical method which is used to show a statement, a system or a theorem is real for each natural number.<br /> The method entails two steps to prove a statement, as mentioned beneath −<br /> <br /></div> <div> </div> <div style="text-align: center;"> <b><u>Example</u></b></div> <div style="text-align: center;"> <div style="font-weight: bold; text-decoration-line: underline;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPngheJlCmenVSLn_1ZVoql3t9sDoYg_wzOBXMG8vuSC6m_y0rERyiACDLBcp3zNi0Pz9WH0tDzxNk4jXIKLdPfUIvt_7qgtv8cFfnfbpweoSgK29WzGttkTN4GbcHmmOUjfMw98hcalnw/s1600/slide_1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPngheJlCmenVSLn_1ZVoql3t9sDoYg_wzOBXMG8vuSC6m_y0rERyiACDLBcp3zNi0Pz9WH0tDzxNk4jXIKLdPfUIvt_7qgtv8cFfnfbpweoSgK29WzGttkTN4GbcHmmOUjfMw98hcalnw/s200/slide_1.jpg" width="200" /></a>Problem 1</div> <div> 3n−13n−1 is a multiple of 2 for n = 1, 2, ...</div> <div> <br /></div> <div> <b>Solution</b></div> <div> <br /></div> <div> <b>Step 1</b> − For n=1,31−1=3−1=2n=1,31−1=3−1=2 which is a multiple of 2</div> <div> <br /></div> <div> <b>Step 2 −</b> Let us assume 3n−13n−1 is true for n=kn=k, Hence, 3k−13k−1 is true (It is an assumption)</div> <div> <br /></div> <div> We have to prove that 3k+1−13k+1−1 is also a multiple of 2</div> <div> <br /></div> <div> 3k+1−1=3×3k−1=(2×3k)+(3k−1)3k+1−1=3×3k−1=(2×3k)+(3k−1)</div> <div> The first part (2×3k)(2×3k) is certain to be a multiple of 2 and the second part (3k−1)(3k−1) is also true as our previous assumption.</div> <div> <br /></div> <div> Hence, 3k+1–13k+1–1 is a multiple of 2.</div> <div> <br /></div> <div> So, it is proved that 3n–13n–1 is a multiple of 2.</div> <div> <br /></div> <div> <b><u>Problem 2</u></b></div> <div> 1+3+5+...+(2n−1)=n21+3+5+...+(2n−1)=n2 for n=1,2,…n=1,2,…</div> <div> <b>Solution</b></div> <div> <br /></div> <div> <b>Step 1</b> − For n=1,1=12n=1,1=12, Hence, step 1 is satisfied.</div> <div> <br /></div> <div> <b>Step 2 </b>− Let us assume the statement is true for n=kn=k.</div> <div> <br /></div> <div> Hence, 1+3+5+⋯+(2k−1)=k21+3+5+⋯+(2k−1)=k2 is true (It is an assumption)</div> <div> <br /></div> <div> We have to prove that 1+3+5+...+(2(k+1)−1)=(k+1)21+3+5+...+(2(k+1)−1)=(k+1)2 also holds</div> <div> <br /></div> <div> 1+3+5+⋯+(2(k+1)−1)1+3+5+⋯+(2(k+1)−1)</div> <div> =1+3+5+⋯+(2k+2−1)=1+3+5+⋯+(2k+2−1)</div> <div> =1+3+5+⋯+(2k+1)=1+3+5+⋯+(2k+1)</div> <div> =1+3+5+⋯+(2k−1)+(2k+1)=1+3+5+⋯+(2k−1)+(2k+1)</div> <div> =k2+(2k+1)=k2+(2k+1)</div> <div> =(k+1)2=(k+1)2</div> <div> So, 1+3+5+⋯+(2(k+1)−1)=(k+1)21+3+5+⋯+(2(k+1)−1)=(k+1)2 hold which satisfies the step 2.</div> <div> <br /></div> <div> Hence, 1+3+5+⋯+(2n−1)=n21+3+5+⋯+(2n−1)=n2 is proved.</div> <div> <br /></div> <div> <b><u>Problem 3</u></b></div> <div> Prove that (ab)n=anbn(ab)n=anbn is true for every natural number nn</div> <div> Solution</div> <div> <br /></div> <div> <b>Step 1 </b>− For n=1,(ab)1=a1b1=abn=1,(ab)1=a1b1=ab, Hence, step 1 is satisfied.</div> <div> <br /></div> <div> <b>Step 2 − </b>Let us assume the statement is true for n=kn=k, Hence, (ab)k=akbk(ab)k=akbk is true (It is an assumption).</div> <div> <br /></div> <div> We have to prove that (ab)k+1=ak+1bk+1(ab)k+1=ak+1bk+1 also hold</div> <div> <br /></div> <div> Given, (ab)k=akbk(ab)k=akbk</div> <div> <br /></div> <div> Or, (ab)k(ab)=(akbk)(ab)(ab)k(ab)=(akbk)(ab) [Multiplying both side by 'ab']</div> <div> <br /></div> <div> Or, (ab)k+1=(aak)(bbk)(ab)k+1=(aak)(bbk)</div> <div> <br /></div> <div> Or, (ab)k+1=(ak+1bk+1)(ab)k+1=(ak+1bk+1)</div> <div> <br /></div> <div> Hence, step 2 is proved.</div> <div> <br /></div> <div> So, (ab)n=anbn(ab)n=anbn is true for every natural number n<br /> <br /> <b><span style="color: red;"><u>Video Tutorial In Urdu</u></span></b><br /> <br /></div> </div> </div> <iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/bieb8A4be5A" width="560"></iframe> </div>

Induction In Discrete Structure By Ishrat Hayat Malik

Induction In Discrete Structure By (Ishrat Hayat Malik) Define :   Induction is a mathematical method which is used to show a statement...

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Program No 9 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> The policy followed via a employer to system purchaser orders is given through the following rules:<br /> <br /> (a) If a client order is much less than or equal to that in stock and has savings is OK, grant has  equirement.<br /> <br /> (b) If has credit score is now not OK do now not supply. Send him intimation.<br /> <br /> (c) If has deposit is Ok but the item in stock is less than has order, provide what is in stock. Intimate to him data the stability will be shipped.<br /> <br /> Write a C application to put into effect the agency policy.<br /> <br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" /></a></div> <span style="background-color: cyan;"><br /></span> <br /> <div> <div> #include<iostream></div> <div> using namespace std;</div> <div> int main()</div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int order , stock;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>char credit;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter available stock: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> stock;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your order: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> order;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "what is your credit status? (y for OK and n for not OK): " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> credit;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span></div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>if(order <= stock && credit == 'y'){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Supply him " << order << " items: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if(credit == 'n'){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "sorry! you can't make order due to your credit status: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>{</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Give him "<< stock <<" and the balance will be shiped as soon as possible -:) " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> }</div> </div> <div> <br /></div> </div>

Program No 9 C++ ( Sir Munawar Ahmed )

The policy followed via a employer to system purchaser orders is given through the following rules: (a) If a client order is much less th...

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Program No 8 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: left;"> A university has the following guidelines for a scholar to qualify for a diploma with A as the principal subject and B as the subsidiary subject:<br /> <br /> (a) He have to get 55 percentage or more in A and forty five percentage or more in B.<br /> <br /> (b) If he gets than fifty five percent in A he need to get fifty five percentage or greater in B. However, he should get at least 45 percentage in A.<br /> <br /> (c) If he gets less than forty five percent in B and 65 percentage or more in A he is allowed to reappear in an examination in B to qualify.<br /> <br /> (d) In all other instances he is declared to have failed.<br /> <br /> Write a software to get hold of marks in A and B and Output whether the pupil has passed, failed or is allowed to reappear in B.<br /> <br /></div> <div style="text-align: left;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" /></a></div> <div style="text-align: left;"> <div> #include<iostream></div> <div> using namespace std;</div> <div> int main()</div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int subject_A;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int subject_B;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your marks obtained in Subject A: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> subject_A;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your marks obtained in Subject B: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> subject_B;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span></div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>if(subject_A >= 55 && subject_B >= 45){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "congratulation! you have passed: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if( subject_A < 55 || subject_A < 45 && subject_B >= 65 ){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Congratulation! You have passed: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if(subject_B <= 45 && subject_A > 65 ){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Please reappear in examination in B to qualify: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "sorry! you are failed: " << endl;</div> <div> }</div> <div> <br /></div> </div> </div>

Program No 8 C++ ( Sir Munawar Ahmed )

A university has the following guidelines for a scholar to qualify for a diploma with A as the principal subject and B as the subsidiary s...

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Program No 7 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: center;"> In a company, employee effectivity is decided on the basis of the time required for a worker to complete a specific job. If the time taken by way of the employee is between 2 – three hours, then the worker is said to be noticeably efficient. If the time required by the worker is between 3 – 4 hours, then the employee is ordered to improve speed. If the time taken is between 4 – 5 hours, the worker is given education to improve his speed, and if the time taken through the worker is greater than 5 hours, then the worker has to leave the company. If the time taken through the worker is enter thru the keyboard, locate the effectivity of the employee </div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" /></a></div> <div style="text-align: left;"> #include<iostream></div> <div style="text-align: left;">  using namespace std;</div> <div style="text-align: left;">  int main()</div> <div style="text-align: left;">  {</div> <div style="text-align: left;">  <span class="Apple-tab-span" style="white-space: pre;"> </span>int hours;</div> <div style="text-align: left;">  <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter the hours of the worker: " << endl;</div> <div style="text-align: left;">  <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> hours;</div> <div style="text-align: left;">  <span class="Apple-tab-span" style="white-space: pre;"> </span>if(hours <= 3){</div> <div style="text-align: left;">  <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Worker is Highly Efficient: " << endl;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> }</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> else if(hours == 4){</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Improve Your speed! " << endl;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> }</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> else if(hours <= 5){</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "You need training to improve your speed: " << endl;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> }</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> else</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> {</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Please leave this company: " << endl;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> }</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span> return 0;</div> <div style="text-align: center;"> <span style="background-color: cyan;"></span></div> <div style="text-align: left;">  }</div> <div style="text-align: center;"> <br /></div> </div>

Program No 7 C++ ( Sir Munawar Ahmed )

In a company, employee effectivity is decided on the basis of the time required for a worker to complete a specific job. If the time taken...

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Program No 6 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: center;"> <span style="background-color: cyan;">If the three facets of a triangle are entered via the keyboard, write a program to test whether the triangle is valid or not. The triangle is legitimate if the sum of two aspects is greater than the largest of the three sides. If the three facets of a triangle are entered via the keyboard, write a software to take a look at whether the triangle is isosceles, equilateral, scalene or right angled triangle. </span></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" /></a></div> <div style="text-align: left;"> #include <iostream></div> <div style="text-align: left;"> using namespace std;</div> <div style="text-align: left;"> int main()</div> <div style="text-align: left;"> {</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>float a, b, c;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<< "enter base of triangle : " ;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin>> a;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<< "enter altitude of triangle : " ;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin>> b;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<< "enter hypotenuse of triangle : " ;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin>> c ;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if ( ( a > b && a > c && b + c > a) || ( b > a && b > c && a + c > b ) || ( c > a && c > b && a + b > c ) )</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"triangle is valid";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>else</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"triangle is not valid";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div style="text-align: center;"> <span style="background-color: cyan;"></span></div> <div style="text-align: left;"> }</div> <div style="text-align: center;"> <br /></div> </div>

Program No 6 C++ ( Sir Munawar Ahmed )

If the three facets of a triangle are entered via the keyboard, write a program to test whether the triangle is valid or not. The triangle...

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Program No 5 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: center;"> <br /> A library fees a pleasant for each and every e book again late. For first 5 days the first-rate is 50 paise, for 6-10 days high-quality is one rupee and above 10 days fantastic is 5 rupees. If you return the e book after 30 days your membership will be cancelled. Write a application to be given the variety of days the member is late to return the  e book and show the first-class or the terrific message. </div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNik1cRDwOJL86SAnVmHs20T6duXcJKEYjgIaqTA9j7yFcuPdNzeqqj-bFxw744IZnkXQ9M6B1YxITNsmhYF1X7U0fzaAVAkwP9wxEqMd5ArirFrYjAb47P1Ri59oArU_hRSyxT63RHdtW/s1600/images.jpg" /></a></div> <div style="text-align: left;"> #include <iostream></div> <div style="text-align: left;"> using namespace std;</div> <div style="text-align: left;"> int main()</div> <div style="text-align: left;"> {</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>int days;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Enter the number of days the member is late to return the  book : ";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin>>days;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if ( days <= 5 )</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Fine applied to the student is 50 paisa";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if ( days > 5 && days < 10 )</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Fine applied to the student is 1 rupee";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if ( days > 10 && days < 30 )</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Fine applied to the student is 5 rupees";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if ( days > 30 )</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Membership has been canceled";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div style="text-align: center;"> <span style="background-color: cyan;"></span></div> <div style="text-align: left;"> }</div> <div style="text-align: center;"> <br /></div> </div>

Program No 5 C++ ( Sir Munawar Ahmed )

A library fees a pleasant for each and every e book again late. For first 5 days the first-rate is 50 paise, for 6-10 days high-quality i...

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Program No 4 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> four A positive grade of metal is graded in accordance to the following conditions:<br /> <br /> (i) Hardness must be increased than 50<br /> <br /> (ii) Carbon content material ought to be much less than 0.7<br /> <br /> (iii) Tensile energy must be larger than 5600<br /> <br /> The grades are as follows:<br /> <br /> Grade is 10 if all three conditions are met<br /> <br /> Grade is 9 if stipulations (i) and (ii) are met<br /> <br /> Grade is eight if prerequisites (ii) and (iii) are met<br /> <br /> Grade is 7 if conditions (i) and (iii) are met<br /> <br /> Grade is 6 if solely one circumstance is met<br /> <br /> Grade is 5 if none of the stipulations are met<br /> <br /> Write a program, which will require the person to supply values of hardness, carbon content and tensile power of the metal below consideration and output the grade of the steel.<br /> <div> <div> #include <iostream><br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-T5iDwvqBcvtIWYfsBv0NsfjO0uh3Whb5wejTA3uO1xc7Ip7Xbv8VirTXgL9RSL9Hq1mKTNOw0WdaEBRo2pDCP9YZZvIkFQ6Iqj-5YYv1UYNwLOLLhlijeVjb9-EIOJ3xsfBA8NAoLy5/s1600/images.jpg" /></a></div> </div> <div> using namespace std;</div> <div> int main()</div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int hardness ;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>float carbon ;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int strength ;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter the value of hardness: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> hardness;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter the value of carbon: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> carbon;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter the value of Strength: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> strength;</div> <div> <br /></div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>if (hardness > 50 && carbon > 0.7 && strength > 5600) {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 10: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (hardness > 50 && carbon > 0.7) {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 9: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (carbon > 0.7 && strength > 5600) {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 8: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (hardness > 50 && strength > 5600) {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 7: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (hardness > 50 || carbon > 0.7 || strength > 5600) {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 6: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Grade is 5: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span></div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>return(0);</div> <div> }</div> </div> <div> <br /></div> </div>

Program No 4 C++ ( Sir Munawar Ahmed )

four A positive grade of metal is graded in accordance to the following conditions: (i) Hardness must be increased than 50 (ii) Carbon ...

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Program No 3 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: left;"> An Insurance corporation follows following policies to calculate premium.<br /> <br /> (1) If a person’s health is remarkable and the individual is between 25 and 35 years of age and lives in a metropolis and is a male then the premium is Rs. four per thousand and his policy quantity cannot exceed Rs. 2 lakhs.<br /> <br /> (2) If a individual satisfies all the above prerequisites besides that the sex is woman then the premium is Rs. 3 per thousand and her coverage quantity cannot exceed Rs. 1 lakh.<br /> <br /> (3) If a person’s fitness is negative and the individual is between 25 and 35 years of age and lives in a village and is a male then the premium is Rs. 6 per thousand and his policy cannot exceed Rs. 10,000.<br /> <br /> (4) In all other cases the individual is no longer insured.<br /> <br /> Write a program to output whether the individual ought to be insured or not, his/her top rate fee and most amount for which he/she can be insured. </div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgLhqo0KgtShjaWOCPXmimIC1ji3NFIGCMoTeLjSdUySH-YLD5wD1OR336Z8KTQ046OQ6spC7xn3sGR1onT6Z5GhHQ_sv3k7WtAwPTsFFXC1pS1d5VsoR5HIlwFfqecLcxovJEozlnJEaQ/s1600/images.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgLhqo0KgtShjaWOCPXmimIC1ji3NFIGCMoTeLjSdUySH-YLD5wD1OR336Z8KTQ046OQ6spC7xn3sGR1onT6Z5GhHQ_sv3k7WtAwPTsFFXC1pS1d5VsoR5HIlwFfqecLcxovJEozlnJEaQ/s1600/images.jpg" /></a></div> <div style="text-align: left;"> <span style="background-color: cyan;"><br /></span></div> <div> <div> #include<iostream></div> <div> using namespace std;</div> <div> int main()</div> <div> {</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>int age;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>char health , location , gender;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your health state (e for excellent and p for poor): " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> health;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your age: " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> age;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Enter your location (c for city and v for village): " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> location;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "Gender (m for male and f for female): " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin >> gender;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span></div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>if( (health == 'e') && (age > 25 && age < 35) && (location == 'c') && (gender == 'm') ){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "The premium is Rs. 4 per thousand and his policy amount cannot exceed Rs. 2 lakhs. " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if((health == 'e') && (age > 25 && age < 35) && (location == 'c') && (gender == 'f') ){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "The premium is Rs. 3 per thousand and her policy amount cannot exceed Rs. 1 lakh. " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if( (health == 'p') && (age > 25 && age < 35) && (location == 'v') && (gender == 'm') ){</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << "The premium is Rs. 6 per thousand and his policy cannot exceed Rs. 10,000. " << endl;</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>}</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>else{</div> <div> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout << " The person in not insured: " << endl;</div> </div> <div> <br /></div> </div>

Program No 3 C++ ( Sir Munawar Ahmed )

An Insurance corporation follows following policies to calculate premium. (1) If a person’s health is remarkable and the individual is b...

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Program No 2 C++ (Sir Munawar Ahmed)

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: center;"> .Any character is entered via the keyboard, write a program to decide whether or not the character entered is a capital letter, a small case letter, a digit or a exclusive symbol. Please seek advice from ASCII Chart.</div> <div style="text-align: center;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLcGpqzgLV0onb9x88KEJ0m2YVDAzG6X3S498HAZxCX1F0OMIRERg_nhyFYjPB63VDgOJ6DZHTaA0tTFbkkAe2iPY_-L2hyLKTtzAyvrOPFw6dTrkxmpsmRAg6xcVdOcQORohsdyWENhXx/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLcGpqzgLV0onb9x88KEJ0m2YVDAzG6X3S498HAZxCX1F0OMIRERg_nhyFYjPB63VDgOJ6DZHTaA0tTFbkkAe2iPY_-L2hyLKTtzAyvrOPFw6dTrkxmpsmRAg6xcVdOcQORohsdyWENhXx/s1600/images.jpg" /></a></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <div style="text-align: left;"> #include<iostream></div> <div style="text-align: left;"> using namespace std;</div> <div style="text-align: left;"> <br /></div> <div style="text-align: left;"> int main ()</div> <div style="text-align: left;"> {</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>char ch;</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Enter any character:";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cin>>ch;</div> <div style="text-align: left;"> <br /></div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>if (ch>=65 && ch<=90)</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Character is a capital letter";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (ch>=97 && ch<=122)</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Character is a small letter";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if (ch>=48 && ch<=57)</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Character is a digit";</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>else if ((ch>0 && ch<=47)||(ch>=58 && ch<=64)||</div> <div style="text-align: left;">                (ch>=91 && ch<=96)||(ch>=123 && ch<=127))</div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>cout<<"Character is a special symbol";</div> <div style="text-align: center;"> <span style="background-color: cyan;"></span></div> <div style="text-align: left;"> <span class="Apple-tab-span" style="white-space: pre;"> </span>return 0;</div> <div style="text-align: left;"> <br /></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> </div>

Program No 2 C++ (Sir Munawar Ahmed)

.Any character is entered via the keyboard, write a program to decide whether or not the character entered is a capital letter, a small ca...

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Program No 1 C++ ( Sir Munawar Ahmed )

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: center;"> <span class="Apple-tab-span" style="background-color: cyan; white-space: pre;"> </span><span style="background-color: cyan;">Any year is entered through the keyboard, write a program to determine whether the year is leap or not. Use the logical operators && and ||.</span></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMLC-GfK9ZmDQte7CnBGoc9nMl0IUCpTt6YFARtEPAhIPMCYBDHDWvFaOBfEQkAzOHcKNMLIdpCs5XVxpyED6CUUyvnZXyfg5l1-pSvcNU6ved8y6js12PX1EqoAYJrxUPcr22ewP1zeVT/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMLC-GfK9ZmDQte7CnBGoc9nMl0IUCpTt6YFARtEPAhIPMCYBDHDWvFaOBfEQkAzOHcKNMLIdpCs5XVxpyED6CUUyvnZXyfg5l1-pSvcNU6ved8y6js12PX1EqoAYJrxUPcr22ewP1zeVT/s1600/images.jpg" /></a></div> <div style="text-align: center;"> <span style="background-color: cyan;"><br /></span></div> <pre style="background: white;"><span style="font-size: 14px;">#include<iostream> using namespace std; int main() { int year; cout << "Enter year: " << endl; cin >> year; if(year % 4 == 0 && year % 2 == 0) { cout << "Leap year: " << endl; } else{ cout << "Not leap year: " << endl; } } // above program also written as // if(year % 4 == 0) // cout << "Leap year " << endl; // if(year % 100 == 0 && year % 400 == 0) // cout << "Leap year" << endl; // else // cout << "not leap year" << endl;</span> </pre> <div> <br /></div> </div>

Program No 1 C++ ( Sir Munawar Ahmed )

Any year is entered through the keyboard, write a program to determine whether the year is leap or not. Use the logical operators &&a...

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