Answer :

It is given that On Z, define a b = a – b

a –b ϵ Z. so the operation * is binary.


We can see that 1 * 2 = 1-2 = -1 and 2 * 1 = 2-1 = 1.


1 *2 ≠ 2 * 1, where 1,2 ϵ Z.


the operation * is not commutative.


Also, we get,


(1 * 2) * 3 = (1 – 2) * 3 = -1 * 3 = -1 -3 = -4


1 * (2 * 3) = 1 * (2 – 3) = 1 * -1 = 1 – (-1) = 2


the operation * is not associative.


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