[(J ⊃ K) • (K ⊃ L)] ⊃ (∼L ⊃ ∼J)
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) [(J ⊃ K) • (K ⊃ L)] ⊃ (∼L ⊃ ∼J)
B) [(J ⊃ K) • (K ⊃ L)] ⊃ ∼L
C) (J ⊃ K) • (K ⊃ L)
D) J ⊃ K
E) J

Question

Quizplus · Accepted Answer

In order to use conditional proof, we need to assume the antecedent of the conditional statement as a premise and try to derive the consequent. Therefore, the proper assumption for conditional proof in this case is the conjunction of the two premises: (J ⊃ K) • (K ⊃ L). Choice A is the actual statement itself, so assuming it as a premise would not help in proof by conditional proof. Choices B, D, and E are all premises that are not sufficient on their own to prove the original statement. Only by assuming (J ⊃ K) • (K ⊃ L) can we begin the conditional proof process.