1. (∀x)[Ex ⊃ (∀y)(Fy • Gxy)]
2. (∃x)(Ex • Hxb)
-Which of the following propositions is derivable from the given premises in F?
A) ~Fb
B) (∀x)Gax
C) (∀x)Gbx
D) (∃x)(∀y)(Gxy ⊃ Hxy)
E) (∃x)(∃y)(Gxy • Hxy)

Question

Quizplus · Accepted Answer

From the given premises, we can derive that there exists at least one x such that Ex and Hxb are true simultaneously due to the second premise. The first premise implies that for all x, if Ex is true, then for all y, Fy and Gxy are true. Combining these, we can infer the existence of at least one x for which Gxy and Hxy are true for some y, specifically for y=b, leading to the conclusion E) (∃x)(∃y)(Gxy • Hxy).

1. (∀X)[Ex ⊃ (∀Y)(Fy • Gxy)]