1. (P $ \lor $ ∼R) ⊃ (P ⊃ Q)
2. P $ \lor $ ∼R
3. P
4. Q ⊃ ∼S
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?
A) ∼R
B) P ⊃ R
C) ∼Q
D) ∼S
E) ∼P

Question

Quizplus · Accepted Answer

We can use Modus Ponens (MP) on premise 1 and premise 3 to get (P ⊃ Q). Then, we can use Modus Tollens (MT) on premise 4 and the previously derived (P ⊃ Q) to get ∼S. Therefore, the correct answer is D.

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

1 (P $\lor$ ∼R) ⊃ (P ⊃ Q)
2 $\lor$