devarshi-dt-logo

Question:

Which one of the following Boolean expressions is a tautology?

(P∧q)∨(p∨¬q)

(P∨q)∧(¬p∨¬q)

(P∨q)∨(p∨¬q)

(P∨q)∧(p∨¬q)

Solution:

(1)(P∨q)∧(¬p∨¬q)≡(p∨q)∧¬(p∧q)→Not tautology (Take both p and q as T)
(2)(p∧q)∨(p∧¬q)≡p∧(q∨¬q)≡p∧t≡p
(3)(p∧q)∧(p∨¬q)≡p∧(q∧¬q)≡p∧c≡c
(4)(p∨q)∨(p∨¬q)≡p∨(q∨¬q)≡p∨t≡t