Q110 / 180 · COMEDK 2020 · Mathematics

Which of the following is not a group with respect to the given operation?

  • Correct answer
    A
    The set of odd integers under addition.
  • B
    The set of even integers under addition.
  • C
    $\{1,-1\}$ under multiplication.
  • D
    $\{0\}$ under addition.

Solution

Option (a) Since, sum of two odd integers is an even integer. Closure property does not hold. So, it is not a group. Option (b) Since, sum of two even integers is an even integer. So, it is a group. Option (c) $1 \times(-1)=-1$, which belongs to given set. So, it is a group. Option (d) $0+0-0$, which belongs to given set. So, it is a group.

Hence, the correct answer is option: 'A'.

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