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Binary Operations — Maths STD 12 Science — Question

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

Answer

Correct option: C.
Not commutative.
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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