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.

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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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