Discrete Mathematics Use inference rules to show that the fo

Discrete Mathematics.

Use inference rules to show that the following Boolean expression is always true (a tautology).

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