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RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
Mark the correct alternative in the following question for the binary operation * on Z defined by a * b = a + b + 1, the identity element is:
  1. 0
  2. -1
  3. 1
  4. 2
✓

Answer

  1. -1
Solution:
We have,
a * b = a + b + 1
Let e be the identity element of *. Then,
a * e = a = e * a
a + e + 1 = a
e = a - a - 1
e = -1

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