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 $R,$ define by $a ^* b = ab^2.$
Here, $Z^+$ denotes the set of all non$-$negative integers.

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Answer

$\text{a, b}\in\text{R}$ Implies that $\text{a, b}^2\in\text{R}$
Implies that $\text{ab}^2\in\text{R}$
Implies that $\text{a}\ ^*\ \text{b}\in\text{R}$
Thus, $^*$ is a binary operation on $R.$

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