How to describe all points with coordinates that are permutations of sets of values for x and y using notation correctly

Question

Suppose I have a set of values for x: something like {1, 2} and another set for y: {3,4}. If I need to list all the possible points which coordinates are permutations of those sets and I don't want to list them explicitly, how would I do it? Best I can do is P(x,y):{x$\in${1,2}, y$\in${3,4}}, but I think it's wrong. How should it be notated correctly?

Answer 1

Say $X=\left\{1,2\right\}$ and $Y=\left\{3,4\right\}$, you're looking for the cartesian product: $$X\times Y=\left\{(x,y):x \in X, y\in Y\right\}=\left\{(1,3),(1,4),(2,3),(2,4)\right\}.$$