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 $a$ * $b=a+4 b^2$
Here, $Z ^{+}$denotes the set of all non-negative integers.

Answer

$\text{a, b}\in\text{R}$$\Rightarrow\ \text{a, 4b}^2\in\text{R}$
$\Rightarrow\ \text{a}+\text{4b}^2\in\text{R}$
$\Rightarrow\ \text{a}\ ^*\ \text{b}\in\text{R} $
Therefore,
$\text{a}\ ^*\ \text{b}\in\text{R},\ \forall\ \text{a, b}\in\text{R}$
Thus, * is a binary operation on R.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free