Question

Write the multiplication table for the set of integers modulo 5.

Answer 1

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

Here we have the operation, a x₅b = remainder of ab divided by 5 where a, b ∈ S.

This is the composition table of x₄ on S = {0, 1, 2, 3, 5}

For example, take 3 x₄ 2 = remainder of (3 x 2) divided by 4

Remainder of \(\frac{6}{4} = 2\)

We also see that the operation x₄ is valid because all the output elements belong to the set S.