#prenex-normal-form

Question 1: Select all that apply

hardAI-checkedKnowledge Representation & Reasoning

$F$ and $P$ are one-place predicates and $G(a)$ is a sentence that does not contain $x$ . Which pairs are logically equivalent? Select all that apply.

$\forall x\,(F(x) \to G(a))$ and $\exists x\, F(x) \to G(a)$ 1
$\forall x\,(F(x) \to G(a))$ and $\forall x\, F(x) \to G(a)$ 2
$\exists x\,(F(x) \to G(a))$ and $\forall x\, F(x) \to G(a)$ 3
$\lnot\forall x\, F(x)$ and $\exists x\, \lnot F(x)$ 4
$\exists x\,(F(x) \land P(x))$ and $\exists x\, F(x) \land \exists x\, P(x)$ 5

Timed test