8. An engineering construction firm is currently working on power plants at three different sites. Let Ai denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1, A2, and A3, draw a Venn diagram, and shade the region corresponding to each one.

a. At least one plant is completed by the contract date.

b. All plants are completed by the contract date.

c. Only the plant at site 1 is completed by the contract date.

d. Exactly one plant is completed by the contract date.

e. Either the plant at site 1 or both of the other two plants are completed by the contract date.