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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