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

Question

Quizplus · Accepted Answer

From premises 3 and 4, we can infer ∼N by Modus Tollens. From premise 1, we can then infer P • ∼R by Disjunctive Syllogism, but we cannot immediately infer N, Q, or ∼Q without further derivation.

1 N ∨ \lor ∨ (P • ∼R) 2

1 N $\lor$ (P • ∼R)
2