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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations1 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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