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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
Let $*$ be a binary operation on $N$ defined by $a^ * b = a + b + 10$ for all $a, b \in N.$ The identity element for $*$ in $N$ is:
  • A
    $−10$
  • B
    $0$
  • C
    $10$
  • ✓
    Non$-$existent.
✓

Answer

Correct option: D.
Non$-$existent.
Given $a^ * b = a + b + 10$
Let the identity element be $e,$ then
$a^ * e = a$
$\Rightarrow a + e + 10 = a$
$\Rightarrow e = -10$
But the operation is defined on the set of natural numbers.
So, the identity element doesn't exist.

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