Question

Given the set definitions below, find X Y. X = {100, 200} Y = {1,2}

Answer 1

The Cartesian product of two sets can be defined as the following: the set of all possible pairs where the 1st coordinate is an element of the 1st set and the 2nd coordinate is the element of the 2nd set. This has an obvious generalization for n sets (the cartesian product has then n coordinates).
Let us pick now all the pairs that have 100 as their first coordinate. We then have 2 choices for the 2nd coordinate, 1 and 2. Hence, the 2 pairs are: (100,1), (100,2). Similarly, if 200 is the first coordinate, the pairs are (200,1), (200,2).
These 4 pairs are the cartesian product (we have 4 pairs =2 elements from X* 2 elements from Y) .
It helps to remember that the cartesian product has as many elements as the product of the number of elements of each set.