For the binary operation x₇ on the set of S = {1, 2, 3, 4, 5, 6} compute 3 ^{– 1}x₇4.

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

Here we have the operation, a x₇b = remainder of ab divided by 7 where a, b S.

For bS to be an inverse of aS, a x₇b = e, where e is the identity element.

We know for multiplication operation we have the identity element as 1.

So e = 1.

For a = 3,

3 x₇ (inverse of 3) = 1

From the table above, 3 x₇ 5 = 1

Hence we can conclude that ‘inverse of 3’ must be 5.

Therefore the expression:

3 ^{– 1} x₇ 4 = 5 x₇ 4 = 6. (From the table above)