A composition table consists of elements which are a result of operation on the set elements.

Here we have the operation, a + ₅ b = remainder of a + b divided by 5 where a, b S.

This is the composition table of x₄ on S = {0, 1, 2, 3, 4}

For example, take 3 + ₅ 2 = remainder of (3 + 2) divided by 5

We also see that the operation + ₅ is valid because all the output elements belong to the set S.