1. (∀x)[Ax ⊃ (∃y)(By • Cxy)]
2. (∃x)(Ax • Dx)
3. (∀x)(Bx ⊃ Ex)
-Which of the following propositions is derivable from the given premises in F?

Question

Quizplus · Accepted Answer

Starting from the first premise:
(∀x)[Ax ⊃ (∃y)(By • Cxy)]
Using universal instantiation:
Aa ⊃ (∃y)(By • Cay)
Looking at the second premise:
(∃x)(Ax • Dx)
Using existential instantiation:
Aa • Da
From here, we can use conjunction elimination to obtain Aa:
Aa
Then, we can use modus ponens to obtain:
(∃y)(By • Cay)
Using existential instantiation:
By • Cay
Using conjunction elimination, we obtain:
Cay
Finally, we can use existential generalization to obtain:
(∃x)[Dx • (∃y)(Ey • Cxy)]
Which matches answer choice A.

1. (∀X)[Ax ⊃ (∃Y)(By • Cxy)]