1. (∀x){Ax ⊃ [Bx • Bf(x)]}
2. ∼Bf(f(e))
-Which of the following propositions is derivable from the given premises in FF?
A) ∼Ae
B) ∼Af(e)
C) Ae
D) Af(e)
E) Bf(e)

Question

Quizplus · Accepted Answer

From premise 1, we know that for all x, if Ax is true, then Bx and Bf(x) are both true. From premise 2, we know that Bf(f(e)) is false. Therefore, we can conclude that Af(e) is false, since it would require both Bf(e) and Bf(f(e)) to be true. This means that its negation, ∼Af(e), is true.

1. (∀X){Ax ⊃ [Bx • Bf(x)]}