$\{(\forall(x))P(x) \implies(\forall(x))Q(x)\} \implies (\forall(x))(P(x) \implies Q(x))$

Question

$(\forall(x))(P(x) \implies Q(x)) \implies \{(\forall(x))P(x) \implies (\forall(x))Q(x) \}$ why this is not valid and how the converse of this is valid?

Answer 1

HINT Consider the statements $x$ is divisible by $4$ and $x$ is divisible by $2$.