Finding relation of two sets

Question

If A = {1, 2, 3} and B = {1, 2, 3, 4}, would R = {(a, b) ∈ A × B | b = a^2} be {(1,1), (2,4)} since the only time that b = a^2 is true is when (A,B) = (1,1) and (A,B) = (2,4)?

Answer 1

Short answer: Yes and you also explained correctly why.

Maybe in other words to help your understanding:

The set $R$ contains all pairs of numbers $(a,b)$ for which $a$ is an element of $A$ and $b$ is an element of $B$ and furthermore the pair must also satisfy the condition $b = a^2$. The pairs you mentioned are the only ones that satisfy these three conditions.