Duality in Logic


In my last post we have seen quantifiers and quantified statements and some of their examples with solution.

In this post 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 duels of given statements.
Two compound statement s1 and s2 are said to be duels 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 duels 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 duels of each other with respect to connectives V and Ʌ. These are called DE Morgan’s laws
Statements (3) and (4) are duels of each other with respect to connectives V and Ʌ. These are called distributive laws.
Ex. Write duels 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 post is on negation of compound statements.

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