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Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations1 Mark
Question
A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is:
  1. Commutative.
  2. Associative.
  3. Not commutative.
  4. Commutative and associative.
✓

Answer

  1. Not commutative.

Solution:

Let $\text{a, b}\in\text{Z}$

a * b = 3a + b

b * a = 3b + a

Thus, a * b $\neq$ b * a

If a = 1 and b = 2,

1 * 2 = 3(1) + 2

= 5

2 * 1 = 3(2) + 1

= 7

1 * 2 $\neq$ 2 * 1

Thus, * is not commutative on Z.

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