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

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)


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