Q. 2 D4.4( 11 Votes )

# For each operatio

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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