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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations1 Mark
Question
The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is:
  1. Commutative only.
  2. Associative only.
  3. Commutative and associative both.
  4. None of these.
✓

Answer

  1. Commutative and associative both.
Solution:
a * b = a + b + ab
b * a = b + a + ba
⇒ a * b = b * a
So * is commutative.
Now,
(a * b) * c
= (a + b + ab) * c
= a + b + ab + c + ca + cb + abc
a * (b * c)
= a * (b + c + bc)
= a + b + c + bc + ab + ac + abc
⇒ (a * b) * c = a * (b * c)
So * is associative.

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