Nested quantifiers order?

Question

$$a) \quad \forall x\exists y(3x+4y=12)$$ $$b) \quad \exists x\forall y(3x+4y=12)$$

Am I correct in saying that a) is correct while b) is false?

Answer 1

You are perfectly correct. The order of the quantifiers does matter (assuming $x$ and $y$ belong to $\mathbb{R}$).