∼(∃x)(Px • Qx) ≡ (∀x)(Px ⊃ ∼Qx)
-Which of the following propositions is also derivable in M given that same assumption?
A) ∼Qx
B) ∼Pa $ \lor $ ∼Qa
C) Px
D) ∼Qx ⊃ Px
E) Pa • Qa

Question

Quizplus · Accepted Answer

In order to derive proposition B, we can first use the equivalence given to rewrite the original proposition as (∀x)(Px ⊃ ∼Qx). We can then instantiate this with a to get Pa ⊃ ∼Qa. From this, we can use De Morgan's law to get ∼(Pa • Qa), which is logically equivalent to ∼Pa $ \lor $ ∼Qa. Therefore, proposition B is derivable in M.

∼(∃X)(Px • Qx) ≡ (∀X)(Px ⊃ ∼Qx) -Which of the Following

∼(∃X)(Px • Qx) ≡ (∀X)(Px ⊃ ∼Qx)
-Which of the Following