How to define the Cartesian Product on $A = \{ x \ | \ P(x)\}$ and $B = \{y \ | \ Q(y)\}$

Question

Let's say I have two sets $A = \{ x \ | \ P(x)\}$ and $B = \{y \ | \ Q(y)\}$, how does one define the cartesian product $A \times B$ on these two sets? Is it simply the following?

$$A \times B = \{(x, y) \ | \ P(x) \land Q(y) \}$$