Find the cardinality of $A =\{(x,y) \in \mathbb R \times \mathbb Q : > x^2 - y = 0 \}\}$
This question may seem trivially easy but I have just started learning about cardinality and still find some things confusing.
My attempt: First of all, I rewrote the definition of the set in a simpler way, adding $y$ to both sides and making necessary assumptions
$$A =\{(x,x^2) : x \in \mathbb R \land x^2 \in \mathbb Q \} = \{(x,x^2) : x\in \mathbb Q \} \cup \{(\pm\sqrt q , q):q \in \mathbb Q \}$$
Now, the cardinality of both of these sets is $\aleph_0$, thus the cardinality of the set in question is $\aleph_o$
Is my solution correct? I not, where have I made a mistake?