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 $\mathrm{Z}^{+}$, define * by a * $\mathrm{b}=\mathrm{a}$
Here, $\mathrm{Z}^{+}$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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