1. ∼R ≡ S
2. T ⊃ R
3. ∼(R $ \lor $ T) ⊃ U
-Consider assuming 'S' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
A) R ≡ ∼S
B) S ≡ R
C) ∼S ≡ ∼ R
D) S ≡ ∼R
E) S ⊃ ∼R

Question

Quizplus · Accepted Answer

Assuming S for conditional proof, from the first premise we get ∼R. Then from the fourth option, we can see that S ≡ ∼R, which is an immediate consequence since we have already shown ∼R to be true under the assumption of S.

1 ∼R ≡ S 2 ∨ \lor ∨ T) ⊃ U -Consider Assuming 'S' for Conditional Proof

1 ∼R ≡ S
2 $\lor$ T) ⊃ U
-Consider Assuming 'S' for Conditional Proof