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

Options

  1. AThe set of odd integers under addition.
  2. BThe set of even integers under addition.
  3. C1,-1 under multiplication.
  4. D0 under addition.

Correct answer

A. The set of odd integers under addition.

Step-by-step 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 (-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.

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