Determine whether the set forms a group with respect to the

Determine whether the set forms a group with respect to the given operation. (You may assume the operation is associative.) If the set does not form a group, determine which properties fail. (Select all that apply.)

The even integers; addition

a.The set forms a group.

b.The closure property fails.

c.The associative property fails.

d.The identity property fails.

e.The inverse property fails.

Solution

Thus, the set of even integers is a group under addition. Option (a) is the correct answer.