There are a variety of ways that a binary relation can be represented: as a listing of all the pairs in the relation, as a graph, as a formula, and so on.

Suppose we have a set $A$ of 4 numbers, 1, 2, 3, and 4, and a set $B$ of 3 letters, a, b, and c. A relation between $A$ and $B$ will be a collection of pairs, where the first component is one of the 4 numbers from $A$ and the second component is one of the 3 letters from $B$. In the left panel of the workspace below, you can choose exactly which pairs are in the relation. The results of your selections will be displayed as a list of pairs in the left panel, and in two graphical representations in the middle and right panels.