1. (∀x)(∃y)Axy ⊃ (∀x)(∃y)Bxy
2. (∃x)(∀y)∼Bxy
-Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
A) (∃y)Axy ⊃ (∀x)(∃y)Bxy
B) ~Bxy
C) (∃x)∼(∃y)Bxy
D) (∀x)(∃y)Bxy
E) (∀y)~Byy

Question

Quizplus · Accepted Answer

From premise 2, we know that there exists an x such that for all y, ~Bxy. This means that there does not exist a y such that Bxy. Therefore, the proposition (∃x)∼(∃y)Bxy is true. This is the only option that can be immediately deduced from the premises.

1. (∀X)(∃y)Axy ⊃ (∀X)(∃y)Bxy