Chapter 9.2, Problem 54E

(a)

To determine

To find: The elements of the set from the mathematical system table.

(b)

To determine

To find: The binary operation of the mathematical system.

(c)

To determine

To check: Whether the system is closed or not.

(d)

To determine

To check: Whether the set having identity element or not.

(e)

To determine

To check: Whether every element in the set having the inverse or not.

(f)

To determine

To give: An example for associative property.

(g)

To determine

To check: The system is commutative or not.

(h)

To determine

To check: The mathematical system is a commutative group under an operation of ‘®’.