Suppose that a number system used only four symbols, a, b, c, and d, and the operation A...

Suppose that a number system used only four symbols, a, b, c, and d, and the operation A; and the system operated as shown in the table. Discuss with your group each of the following:

a. Is the system closed? Why?

b. Is the operation commutative? Why?

c. Does the operation have an identity? If so, what is it?

d. Try several examples to investigate the associative property of this operation.