Question

Let r ∈ {p , q , ~p , q} be such that the logical statement r ∨ (p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :

• A. p
• B. q
• C. ~p
• D. ~q

Answer 1

Answer: (C)

~p

Answer 2

The correct answer is (C) : ~p
Clearly r must be equal to ~ p
∵ ~ p ∨ ~ p = ~ p
and (p ∧ q) ∨ ~ p = p
∴ ~ p ⇒ p = tautology.