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
Here, Z⁺ denotes the set of all non-negative integers.

✓

Answer

$\text{a, b}\in\text{Z}^{+}$

$\Rightarrow\ \text{a}\in\text{Z}^{+}$

$\Rightarrow\ \text{a}\ ^*\ \text{b}\in\text{Z}^{+}$

Therefore,

$\text{a}\ ^*\ \text{b}\in\text{Z}^{+},\ \forall\ \text{a, b}\in\text{Z}^{+}$

Thus, * is a binary operation on Z⁺.

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