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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Find which of the binary operations are commutative and which are associative.
Consider a binary operation * on N defined as a * b = a3 + b3. Choose the
correct answer.
  1. Is * both associative and commutative?
  2. Is * commutative but not associative?
  3. Is * commutative but not associative?
  4. Is * neither commutative nor associative?
✓

Answer

a * b = a3 + b3 = b3 + a3 = b * a
$\therefore$ The operation is commutative.
Again, (a * b) * c = a * (a3 + b3) = a3(a3 + b3)3
And (a * b) * c= (a3 + b3) * c = (a3 + b3)3 + c3 $\neq\text{a}*(\text{b}*\text{c})$
$\therefore$ The operation * is not associative.
 Therefore, option (B) is correct.
  1. Is * commutative but not associative?

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