1. (∀x)(Jx ⊃ Kx)
2. ∼(∀x)Kx
3. ∼(∀x)Ix $ \lor $ (∀x)Jx
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?
A) ∼Kx
B) Ja ⊃ Kc
C) ∼(∀x)Ix $ \lor $ ∼(∃x)∼Jx
D) ∼(∃x)∼Ix $ \lor $ (∀x)Jx
E) Kx

Question

Quizplus · Accepted Answer

The proposition ∼(∀x)Ix $ \lor $ ∼(∃x)∼Jx is an immediate consequence because it is logically equivalent to the given premise 3, ∼(∀x)Ix $ \lor $ (∀x)Jx, by the negation of the existential quantifier.

1 (∀X)(Jx ⊃ Kx) 2 ∨ \lor ∨ (∀X)Jx -Which of the Following Propositions Is an Immediate (One-Step)

1 (∀X)(Jx ⊃ Kx)
2 $\lor$ (∀X)Jx
-Which of the Following Propositions Is an Immediate (One-Step)