The domain of discourse $\mathbb R \times \mathbb R$.

Q: $\forall x\,\forall y (x^2 < y+1)$

Answer given by book: False by counterexample, $x=3, y=0$ 

The book says "to prove $∀x\,∀y P(x,y)$ is false, where the discourse $X \times Y$, find one value of $x$ subset of $X$ and one value for $y$ subset of $Y$ to make $P(x, y)$ false"

**But why? I cannot seem to understand the logics behind the answer nor the explanation.**

The way I think about the problem for every real number $x$ and every real number $y$ such that when $1$ added to $y$ is greater than $x^2$.

Therefore, I conclude that the statement will always be true. The answer above is wrong since $y$ can be $9$, so $9 < 9+1$ is true...

Thank you