1. (∀x)Ix ⊃ (∀x)Kx
2. (∀x)[Jx • (Ix $ \lor $ Lx)]
3. (∀x)(Jx ⊃ ∼Lx)
-Which of the following propositions is derivable from the given premises in M?
A) (∃x)∼Jx
B) (∃x)Lx
C) (∀x)Lx
D) (∀x)Kx
E) (∀x)∼Jx

Question

Quizplus · Accepted Answer

From the premises, we can derive that (∀x)Kx. Here's a brief explanation: 1. From the second premise, we know that for all x, Jx and (Ix or Lx). 2. The third premise tells us that for all x, if Jx then not Lx, which means for all x, we have Jx and Ix (since Lx leads to a contradiction with Jx).3. Given that for all x, Ix (from step 2), and the first premise states that if for all x, Ix then for all x, Kx, we can conclude that (∀x)Kx.

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