Determine which properties the given mathematical system exhibits. Identify any systems that are
Groups or Abelian groups.
A)closure, commutative, identity, inverse, associative; Abelian group
B)closure, commutative
C)closure, commutative, identity
D)closure, commutative, identity, inverse

Question

Determine which properties the given mathematical system exhibits. Identify any systems that are
Groups or Abelian groups. 
A)closure, commutative, identity, inverse, associative; Abelian group 
B)closure, commutative 
C)closure, commutative, identity 
D)closure, commutative, identity, inverse

Quizplus · Accepted Answer

The mathematical system exhibits all five properties (closure, commutative, identity, inverse, associative) and is also Abelian, meaning it is commutative. No other system mentioned exhibits all five properties or is Abelian. The system in option A exhibits all the necessary properties of a group: closure (because of associative operation), commutativity, identity element, inverse element, and associativity. Furthermore, the group is Abelian because the operation is commutative. Options B, C, and D lack one or more of the necessary properties of a group.

Determine Which Properties the Given Mathematical System Exhibits