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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations1 Mark
Question
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is:
  1. −10
  2. 0
  3. 10
  4. Non-existent.
✓

Answer

  1. Non-existent.
Solution:
Given a * b = a + b + 10
Let the identity element be e, then
a * e = a
⇒ a + e + 10 = a
⇒ e = -10
But the operation is defined on the set of natural numbers.
So, the identity element doesn't exist.

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