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Question:

(p∧q↔r) is true and q is false, then which one of the following is a tautology?

p∨r

p∧r

(q∨r)→(p∧r)

(p∨r)→(p∧r)

Solution:

Given q is F and (p∧q)↔r is T ⇒ p∧q is F which implies that r is F ⇒ q is F and r is F ⇒ (q∨r) is always F ⇒ (q∨r)→(p∧r) is a tautology.