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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations2 Marks
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+, defined * by a * b = ab.
Here, Z+ denotes the set of all non-negative integers.
✓

Answer

$\text{a, b}\in\text{Z}^{+}$

$\Rightarrow\ \text{ab}\in\text{Z}^+$

$\Rightarrow\ \text{a}\ ^*\ \text{b}\in\text{Z}^+$

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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