An engineering construction firm is currently working on powerplants at 3 different sites. Let Ai donate the even 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 that correspond to each one.

Part A: At least one plant is completed by the contract date.

Part B: All plants are completed by the contract date.

Part C: Only the plant at site #1 is completed by the contract date.

Part D: Exactly one plant is completed by the contract date.

Part E: Either the plant at site #1, or both of the other two palnts are completed by the contract date.

Part A: A1 U A2 U A3

Part B: A1 n A2 n A3

Part C: A1 n A2' n A3'

Part D: (A1 n A2' n A3') U (A1' n A2 n A3') U (A1' n A2' n A3')

Part E: A1 U (A2 n A3)

Explanation: A set is the collection of objects with definite properties. The events Ai that describe the completion of a contract can be described as a set.

By Union of a set, U, we mean the set that contains all the elements that belong to A1, A2 and A3 or all.

By Intersection of sets,n, we mean the set that contains or are common to each of the events A1, A2 or A3.

By Compliment of a set ('), we mean all the elements in the universal set, but not in either A1, A2 or A3.

Hence, for the given question,

Part A: A1 U A2 U A3

Part B: A1 n A2 n A3

Part C: A1 n A2' n A3'

Part D: (A1 n A2' n A3') U (A1' n A2 n A3') U (A1' n A2' n A3')

Part E: A1 U (A2 n A3). Find attached Venn diagram.

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