Determine whether the given system forms (a)a group and (b)an Abelian group.
Even integers under addition
A)a group but not an Abelian group
B)not a group
C)Abelian group
D)Abelian group but not a group

Question

Quizplus · Accepted Answer

For a set to form a group under a given operation, it must satisfy four conditions: closure, associativity, identity element, and inverse element.

In this case, the set of even integers under addition satisfies all four conditions, so it forms a group.

Furthermore, the operation of addition is commutative in this set, since adding two even integers always gives an even integer, which ensures that the group is Abelian. Therefore, the answer is (C) Abelian group.

Determine Whether the Given System Forms (A)a Group and (B)an