Q. 9 D5.0( 4 Votes )

Let be a binary operation on the set Q of rational numbers as follows:

a b = (a – b)2

Find which of the binary operations are commutative and which are associative.

Answer :

It is given that be a binary operation on the set Q of rational numbers is defined as

a b = (a – b)2


For a, b ϵ Q, we have,


a b = (a – b)2


b a = (b – a)2 = [-(a – b)]2 = (a –b)2


a * b = b * a


the operation * is commutative.


Also, We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q


Therefore, the operation * is not associative.


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