1. ∼J ⊃ K
2. K ⊃ (L ⊃ M)
3. J ⊃ M
4. ∼M
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?
A) ∼K
B) J
C) ∼M ⊃ L
D) ∼L
E) L

Question

Quizplus · Accepted Answer

Starting with premise 3, J ⊃ M, and using Modus Tollens with premise 4, we can conclude ∼J. Then, using Modus Ponens with premises 1 and ∼J, we can derive ∼K. Finally, using Modus Ponens with premise 2 and ∼K, we can derive ∼(L ⊃ M), which is equivalent to ∼L. Therefore, the correct answer is D, ∼L.