1. P ≡ Q
2. ∼Q
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A) (P ⊃ Q) • (Q ⊃ P)
B) (P ⊃ Q) $ \lor $ (Q ⊃ P)
C) (P • Q) • (∼P • ∼Q)
D) (P $ \lor $ Q) • (∼P $ \lor $ ∼Q)
E) ∼P ≡ Q

Question

Quizplus · Accepted Answer

The correct answer is A because it is the only proposition that is an immediate consequence of the given premises. The other propositions are not immediate consequences of the given premises.

1 P ≡ Q 2 ∨ \lor ∨ (Q ⊃ P) C) (P • Q) • (∼P •

1 P ≡ Q
2 $\lor$ (Q ⊃ P)
C) (P • Q) • (∼P •