1. J ⊃ (K ⊃ L)
2. M ⊃ K
3. M ⊃ J
4. M • K
-Which of the following propositions is derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?
A) J
B) K
C) L
D) All of the above
E) Options A and B, but not option C

Question

Quizplus · Accepted Answer

Given the premises and using the rules of inference, we can derive all of the options (J, K, L). Starting with premise 4 (M • K), we can use Simplification (Simp) to derive K directly. Using Modus Ponens (MP) with premises 2 (M ⊃ K) and 3 (M ⊃ J), we can derive J since M implies both K and J. Finally, using Hypothetical Syllogism (HS) with premises 1 (J ⊃ (K ⊃ L)) and our derived J, we can conclude K ⊃ L, and then using MP with our derived K, we can conclude L. Therefore, all of the options A, B, and C (J, K, L) are derivable, making D the correct answer.