Cartesian product
A x B is the set of all possible pairs of elements (a,b) where a∈A and b∈B.
So each pair is an element in this set. The pairs are ordered: in general (a,b) ≠ (b,a). The pairs could be, for example, coordinates of a point in the Cartesian plane. (note the name - it is why the cartesian product is named what it is).
If A and B are finite then size(A x B) = size(A) x size(B)
As an example, to help visualise it, consider A = {1,2,3} and B={f,g}. Then A x B has 6 elements as follows:
| set B | |||
| f | g | ||
| set A | 1 | (1,f) | (1,g) |
| 2 | (2,f) | (2,g) | |
| 3 | (3,f) | (3,g) | |