The operation Θ is defined on the set S = {a, b, c}, as shown in the following table. For...

The operation Θ is defined on the set S = {a, b, c}, as shown in the following table. For example, a Θ b = b and b Θ a = b.

a. Is S closed with respect to Θ ?

b. Is Θ commutative on S?

c. Is there an identity for Θ on S? If yes, what is it?

d. Try several examples to investigate the associative property for Θ on S.