An engineering construction rm is currently working on power plants at three di erent sites. Let A1 denote the event that the plant at site 1 is completed by the contract date, let A2 denote the event that the plant at site 2 is completed by the contract date, and let A3 denote the event that the plant at site 3 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.
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.