Understanding Duality in Logic 📚

Duality in Logic<br />Hello friends, I am Anil Kore, welcome to my channel mathstips4u.<br />In my last video we have seen quantifiers and quantified statements and some of their examples with solution.<br />In this video we are going to learn duality in logic with some examples.<br />This is most simple part in this topic but I do not understand <br />that some students do not write properly the dual of given statements. <br />Two compound statement s1 and s2 are said to be dual of each other if one can be obtained from other by replacing Ʌ by V and T by F and c by t and vice versa where t denote tautology and c denote contradiction. <br />Note: while obtaining dual the symbol ~ is not changed.<br />e.g. 1) ~ (p V q) = ~ p Ʌ ~q<br />2) ~ (p Ʌ q) = ~ p V ~q<br />3) p V (q Ʌ r) = (p V q) Ʌ (p V r)<br />4) p Ʌ (q v r) = (p Ʌ q) V (p Ʌ r)<br />Statements (1) and (2) are dual of each other with respect to connectives V and Ʌ. These are called DE Morgan’s laws<br />Statements (3) and (4) are dual of each other with respect to connectives V and Ʌ. These are called distributive laws.<br />Ex. Write duals of the following statements<br />1) p Ʌ [~q V (p Ʌ q) V ~r]<br />2)(p V t) Ʌ (c V ~q)<br />3) (p Ʌ q) V F<br />4) Anil or Sunil went to Mumbai.<br />5) He is tall and handsome.<br />Answers: -<br />1) p V [~q Ʌ (p V q) Ʌ~r]<br />2)(p Ʌ c) V (tɅ~q)<br />3) (p V q) ɅT<br />4) Anil and Sunil went to Mumbai.<br />5) He is tall or handsome.<br />Isn’t a simple?<br />In this way we have seen duality in logic.<br />My next video is on negation of compound statements.<br />Thanking you for watching my video.<br />