Repeat parts (a)–(h) of  for the mathematical system defined by the given table. Assume that the associative property holds for the given operation.

(a) What are the elements of the set in this mathematical system? 

(b) What is the binary operation? 

(c) Is the system closed? Explain. 

(d) Is there an identity element in the set? If so, what is it?

(e) Does every element in the set have an inverse? If so, give each element and its corresponding inverse.

(f ) Give an example to illustrate the associative property.

(g) Is the system commutative? Give an example to verify your answer.

(h) Is the mathematical system a commutative group? Explain.

Transcribed Image Text:

3 8 4 5 5 4 5 3 5 3. 4, 3. 4- 3. 4. 4,