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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations2 Marks
Question
Determine whether the following operations define a binary operation on the given set or not:
$'*'$ on N defined by $a * b = a^b$ for all $\text{a, b}\in\text{N.}$
✓

Answer

Let $\text{a, b}\in\text{N}$
Then, $\text{a}^{\text{b}}\in\text{N}$ $\big[$Therefore $\text{a}^{\text{b}}\neq0$ and $a^b$ is positive integer$\big]$
Implies that $\text{a}\ ^*\ \text{b}\in\text{N}$
Therefore, $\text{a}\ ^*\ \text{b}\in\text{N},\ \forall\ \text{a, b}\in\text{N}$
Thus, $*$ is a binary operation on $N.$

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