[(P $ \lor $ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]
Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?
A) [(P $ \lor $ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]
B) [(P $ \lor $ Q) ⊃ R] ⊃ (S ⊃ Q)
C) [(P $ \lor $ Q) ⊃ R] ⊃ S
D) (P $ \lor $ Q) ⊃ R
E) (P $ \lor $ Q

Question

Quizplus · Accepted Answer

To prove the given wff is a logical truth, we need to assume its antecedent as true and derive its consequent as true using the rules of inference. So, we need an assumption that implies the given wff. Out of the given options, (D) is the only assumption that implies the given wff. Therefore, we need to assume (P $ \lor $ Q) ⊃ R and derive the given wff as a consequent. Note that the other options do not imply the given wff, so they are not suitable assumptions for conditional proof.

[(P ∨ \lor ∨ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)] Which

[(P $\lor$ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]
Which