Solving truth value of predicate calculus statements(Just the approach)

Question

Which of the following predicate calculus statements is/are valid?

1. $$\forall x, P(x)\lor \forall x,Q(x) \Rightarrow \forall x, (P(x)\lor Q(x))$$

2. $$\exists x, P(x)\land \exists x, Q(x) \Rightarrow \exists x, (P(x)\land Q(x)) $$

3. $$\exists x, P(x)\land \exists x, Q(x) \Rightarrow \forall x, P(x)\lor \forall x,Q(x)$$

4. $$\exists x, (P(x)\lor Q(x)) \Rightarrow \forall x, P(x)\lor \exists x,Q(x)$$

What is the approach to solve these questions? I have learned that one way to solve these questions is to consider a $P(x)$ say "all numbers are odd" and $Q(x)$ say "all numbers are even", and then reason out with each option to see which one is true.
Being a CS freshman I have had a hard time understanding these,so can anyone explain to me in a straightforward fashion.
Also is there any mechanical(algebraic) way to solve these using propositional logic rules?