Use inference rules to show that the following Boolean expre

Use inference rules to show that the following Boolean expression is always true (a tautology). [(p Lambda not(not p V q) V (p Lambda q))] rightarrow p

Solution

Tautology :-

A Boolean expression is a tautology if and only if for all possible assignments of truth values to its variables its truth value is True.

Solution :-

Given Boolean Expression :- (( P & ¬( ¬P Q)) (P & Q)) P

Let us consider...

( P & ¬( ¬P Q)) = A

(P & Q) = B

Therefore... (( P & ¬( ¬P Q)) (P & Q)) = A B

Finally... (( P & ¬( ¬P Q)) (P & Q)) P =  (A B) P

Truth Table

P	¬P	Q	(¬PQ)	¬(¬PQ)	A	B	A B	(A B) P
True	False	True	True	False	False	True	True	True
True	False	False	False	True	True	False	True	True
False	True	True	True	False	False	False	False	True
False	True	False	True	False	False	False	False	True