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

Question

Quizplus · Accepted Answer

From premise 1, we can use modus ponens with premise 3 to get P ⊃ Q as our immediate consequence.

1 (P ∨ \lor ∨ ∼R) ⊃ (P ⊃ Q) 2 ∨ \lor ∨

1 (P $\lor$ ∼R) ⊃ (P ⊃ Q)
2 $\lor$