Answer :

It is given that on Z+, define a b = 2ab

2abϵ Z+, so operation * is binary


We know that ab = ba for a,b ϵ Z+


2ab = 2ba for a,b ϵ Z+


a * b = a * b for a, b ϵ Z+


The operation * is commutative.


Also, we get,


(1 * 2) * 3 = 2(1×2) *3 = 4 * 3 = 2(4×3) = 212


1 * (2 * 3) = 1 * 2(2 × 3) = 1 * 26 = 1 × 64 =264


(1 * 2) * 3 ≠ 1 * (2 * 3)


The operation * is not associative.


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