Construct the composition table for `xx_4` on set `S={0,\ 1,\ 2,\ 3}` .

Explanation

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

Here we have the operation, `a \ x_{4} b=` remainder of `a b` divided by 4 where `a, b in S`.





` x_{4} \ \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3`


`\ 0 \ \ \ \ \ \ 0 \ x_4\ 0 =0 \ \ \ \ \ \ 1 \ x_4\ 0 =0 \ \ \ \ \ \ 2 \ x_4\ 0 =0 \ \ \ \ \ \ 3 \ x_4\ 0 =0`


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