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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations1 Mark
MCQ
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:
  • A
    0
  • ✓
    -1
  • C
    1
  • D
    2
✓

Answer

Correct option: B.
-1
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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