Counterexample for the logical argument

Question

Give a counter example to show the argument is not valid by using formulas from a particular structure interpreting the language.

$\forall x\exists y (r_1xy)$

$\forall y \exists x (r_2xy)$

then, $\forall x \exists y ((r_1xy)\wedge (r_2xy))$

Answer 1

Let the universe be $\mathbb{N}$, $r_1$ denotes $=$, and $r_2$ denotes $\neq$.