Duality in Logic

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