Q9 of 107 Page 24

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

a ∗ b =


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

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

a ∗ b =


For a, b ϵ Q, we get,


a * b = = b * a


⇒ the operation is commutative.


For a, b, c ϵ Q, we get,


(a * b) * c =


a * (b * c) = a *


⇒ (a * b) * c = a * (b * c)


Therefore, the operation * is associative.


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