Determining truth value of statement with more than one quantifier

Question

Domain: $\{1, 2, 3, 4\}$
Referents: $a: 3, b: 4$
Extensions: $M:\{1, 2\}, F:\{3, 4\}, J:\{1, 3\}, S:\{2, 4\}$

How can I determine the truth value if there is more than one quantifier applied to the same expression? For example, how to determine the truth value of these four expressions:

1. $\forall x \forall y(Mx \implies My)$
   
2. $\forall x \exists y(Jy \iff Sx) \lor Jb$
   
3. $\exists x \exists y(Jx \lor Fy \lor My)$
   
4. $\exists y \forall x(Sy \iff Mx) \land Ja$
   

Answer 1

Let's do a simpler example, assume the domain is simply $\{ 1,2 \}$ and evaluate $\forall x \exists y \ (Mx \land My)$

You can work this out one quantifier at a time. First the universal:

$\exists y (M1 \land My) \land \exists y (M2 \land My)$

And now both existentials:

$((M1 \land M1) \lor (M1 \land M2)) \land ((M2 \land M1) \lor (M2\land M2))$