The statement [ (p q ) ∧ ∼q ] r is a tautology, when r is equivalent to

Question

Accepted Answer

Correct answer: D. (d) : [ (p q ) ∧ ∼q ] r ≡ [ ( ∼p ∨q ) ∧ ∼q ] r ≡ [ ( ∼p ∧ ( ∼q ) ∨ (q ∧ ( ∼q ) ) ] r ≡ [ ( ( ∼p ) ∧ ( ∼q ) ∨ ] r ≡ ( ( ∼p ) ∧ ( ∼q ) ) r ≡ ( ∼ ( ∼p ∧ ( ∼q ) ) ) ∨r ≡ (p ∨q ) ∨r p q p ∨q ∼q (p ∨q ) ∨ ( ∼q ) T T T F T T T T F T T F T T T T F T T T F T T F T F T T F T F F F T T F F F T T ⇒ (p ∨q ) ∨ ( ∼q ) is a tautology, so r must be equivalent to ∼q.

$The statement [(p \to q) \land \sim q] \to r is a tautology, when r is equivalent to$

Solution

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