$1.\left \{ \exists x A(x),\forall x \,\,\, \text{ }^{'} \left \{ A(x) \wedge Q(x) \right \} \Rightarrow \exists x Q(x)\right \}$
can be wriiten as
$1.\left \{ \exists x A(x) \wedge \text{ }^{'} \, \exists x \left \{ A(x) \wedge Q(x) \right \} \Rightarrow \exists x Q(x)\right \}$
To check the validity of the logic ,we need to prove
True $\Rightarrow$True
for LHS to be true,
$\exists x A(x)$ must be true
AND
$\left \{ A(x) \wedge Q(x) \right \}$ must be false so that ¬false=true
and then true AND true=TRUE
As $\left \{ A(x) \wedge Q(x) \right \}$ must be false and we know already $\exists x A(x)$ must be true
so $\exists x Q(x)$ must be false but RHS says $\exists x Q(x)$ is true hence true $\Rightarrow$ false .hence whole logic is invalid
so same for part 2
