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

Question

Quizplus · Accepted Answer

BA) From premise 3, we can infer that for all x, it is not the case that both Jx and Kx are true, which is a restatement of the negation of the existential quantifier in premise 3.B) Premise 3 directly states that there does not exist an x such that both Jx and Kx are true, which is the same as saying it is not the case that Jx and Kx for any particular instance of x.

1. (∃X)(Hx • ∼Ix)