1. J ⊃ K
2. ∼J $ \lor $ L
3. (K • L) ≡ M
-Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?
A) J ⊃ ∼K
B) J ⊃ ∼L
C) J ⊃ M
D) M ⊃ J
E) None of the above

Question

Quizplus · Accepted Answer

Starting with premise 1 and 2, we can use Modus Tollens to derive ∼K ∨ ∼L. Then we use De Morgan's law to get ∼(K • L), which is equivalent to ∼M. From premise 3, we know that (K • L) ≡ M. Therefore, if we use a biconditional syllogism, we can infer (K • L) ≡ ∼(K • L), which simplifies to K ≡ ∼L. Finally, we can use Modus Tollens again with premise 1 to derive J ⊃ ∼K, and use the biconditional we just derived to convert this to J ⊃ ∼L. 
Thus, the correct answer is C, J ⊃ M.

1 J ⊃ K 2 ∨ \lor ∨ L 3 (K • L) ≡ M -Which of the Following

1 J ⊃ K
2 $\lor$ L
3 (K • L) ≡ M
-Which of the Following