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

Question

Quizplus · Accepted Answer

The first premise states that there does not exist an x such that Ax is true. The second premise states that if for all x, Ax is not true, then there does not exist an x such that Bx is true. From these, an immediate consequence is that if there does not exist an x such that Ax is true (which is given in the first premise), then there does not exist an x such that Bx is true, which matches option E. This follows directly from the structure of the second premise when considering the truth of the first premise.

1. ∼(∃X)Ax 2. (∀X)∼Ax ⊃ ∼(∃X)Bx