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in Sets, Relations and Functions by (9.2k points)

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

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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 b  S to be an inverse of a  S, 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

Remainder of \(\frac{3(i)}{7}\) = 1, i is the inverse of 3.

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)

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