Q2 of 107 Page 24

For each operation ∗ defined below, determine whether ∗ is binary, commutative or associative.

On Q, define a ∗ b =

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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