COMEDK · Maths · 24. Functions
Which of the following is not a group with respect to the given operation?
- 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.
Answer & Solution
Correct Answer
(A) The set of odd integers under addition.
Step-by-step Solution
Detailed explanation
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.…
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