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Binary Operations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinary Operations1 Mark
MCQ
A binary operation $*$ on $Z$ defined by $a * b = 3a + b$ for all $a, b \in Z,$ 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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