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

Question

Quizplus · Accepted Answer

From premise 2, we can use double negation elimination to get ∼Q, which combined with premise 1 gives us P ⊃ Q. From there, we can use modus tollens with premise 4 to get ∼P. Finally, we can use modus ponens with P ⊃ Q and ∼P to get ∼Q, which combined with premise 2 gives us R. Therefore, ∼R is an immediate consequence.

1 P ⊃ ∼Q 2 ∨ \lor ∨ ∼∼Q 3 R ⊃ S 4

1 P ⊃ ∼Q
2 $\lor$ ∼∼Q
3 R ⊃ S
4