1. (∀x)[(Px • Qx) ⊃ Rf(x)]
2. (∀x)[Rx ⊃ (∃y)Pxy]
3. ∼(∀x)(Px ⊃ ∼Qx)
-Which of the following propositions is derivable from the given premises in FF?
A) (∀x)[Pf(x) ⊃ Qf(x)]
B) (∀x)Rf(x)
C) (∀x)Rf(f(x))
D) (∃x)(∃y)Pf(x)f(y)
E) (∃x)(∃y)Pxy

Question

Quizplus · Accepted Answer

The third premise negates the implication that Px implies not Qx, suggesting there exists some x for which Px and Qx are both true. This aligns with the existential quantifier in option E.

1. (∀X)[(Px • Qx) ⊃ Rf(x)]