Determine whether or not the definition of * given below gives a … - Vidyadip

Question

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On Z⁺ define * by a * b = |a - b|
Here, Z⁺ denotes the set of all non-negative integers.

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Answer

On Z⁺, * is defined by a * b = |a - b|.

It is seen that for each $\text{a, b}\in\text{Z}^{+},$ there is a unique element |a - b| in Z⁺.

This means that * carries each pair (a, b) to a unique element a * b = |a - b| in Z⁺.

Therefore, * is a binary operation.

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