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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.
The identity element for the binary operation * defined on $\text{Q}\sim\{0\}$ as $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2}\ \forall\ \text{a, b}\in\text{Q}\sim\{0\}$ is:
  1. 1
  2. 0
  3. 2
  4. none of these.
✓

Answer

  1. 2

Solution:

Given that, $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2}\ \forall\ \text{a, b}\in\text{Q}\sim\{0\}$

Let e be the identity element for *

$\therefore\ \text{a}\ ^*\ \text{e}=\frac{\text{ae}}{2}(\text{a}\ *\ \text{e}=\text{e}\ *\ \text{a}=\text{a})$

$\Rightarrow\ \text{a}=\frac{\text{ae}}{2}$

$\Rightarrow\ \text{e}=2$

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