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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is:
  1. $1$
  2. $\frac{\text{a}-1}{\text{a}}$
  3. $\frac{\text{a}}{\text{a}-1}$
  4. $0$
✓

Answer

  1. $0$

Solution:

Let e be the identity element in Q - {1} with respect to * such that

a * e = a = e * a, $\forall\text{ a}\in\text{Q}-\{-1\}$

a * e = a and e * a = a, $\forall\text{ a}\in\text{Q}-\{-1\}$

a + e - ae = a and e + a - ea = a, $\forall\text{ a}\in\text{Q}-\{-1\}$

e(1 - a) = 0, $\forall\text{ a}\in\text{Q}-\{-1\}$ $[\because \text{a}\neq1]$

Thus, 0 is the identity element in Q - {1} with respect to *.

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