Answer :

It is given that On Q, define a b =

Now, ϵ Q, so the operation * is binary.


We know that ab = ba for a,b ϵ Q


= for a, b ϵ Q


a * b = a * b for a,b ϵ Q


The operation * is commutative.


Also for all a,b,c ϵ Q, we get,


(a * b) * c = () * c =


a * (b * c) = a * () =


(a * b) * c = a * (b * c)


the operation * is associative.


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