A relation describes certain relationship between two things. For example, we say someone is the father of another person, Monrovia is the capital city of Liberia, 10 is a multiple of 2, etc. In mathematics, we usually look for a relation between elements of two sets and use ordered pair to describe related elements. For example, let

A = {Monrovia, Paris, Abuja, Addis Ababa} and

B = {China, Ethiopia, Liberia, Nigeria}.

For x ∈ A and y ∈ B, if x and y in the ordered pair (x, y) are related by the phrase

“x is the capital city of y”,

then the relation can be described by the following set of ordered pairs:

{(Monrovia, Liberia), (Abuja, Nigeria), (Addis Ababa, Ethiopia)}.

Each pair is ordered so as to fit to the phrases (the statement) that describe the relation and should make the statement true. For example, according to the statement of the given relation, the pair (Monrovia, Liberia) means “Monrovia is the capital city of Liberia” which is true.

In general, relation is the set of ordered pairs. Thus, as ordered pairs are elements of the Cartesian product of two sets, it is important to recall the notion of Cartesian product. The following activity is helpful for this purpose.