1) Determine if $\displaystyle \forall x(P(x) \rightarrow Q(x)) $ and $\displaystyle \forall xP(x) \rightarrow \forall xQ(x)$ are logically equivalent. Justify your answers.

2) Determine if $\displaystyle \forall x(P(x) \leftrightarrow Q(x)) $ and $\displaystyle \forall xP(x) \leftrightarrow \forall xQ(x)$ are logically equivalent. Justify your answers.

3) Show that $\displaystyle \exists x(P(x) \vee Q(x))$ and $\displaystyle \exists xP(x) \vee \exists xQ(x)$ are logically equivalent.

I'm getting confused with these. Please explain me in a simpliest way. Thank you very much for your help.