6.11 An engineering construction firm is currently working on power plants at three different sites. Define events E1, E2, and E3 as follows:

E1 5 the plant at Site 1 is completed by the contract date E2 5 the plant at Site 2 is completed by the contract date E3 5 the plant at Site 3 is completed by the contract date The following Venn diagram pictures the relationships among these events:

E1 E2 E3 Shade the region in the Venn diagram corresponding to each of the following events. Redraw the Venn diagram for each part of the problem. (Hint: See the discussion of Venn diagrams)

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

b. All plants are completed by the contract date.

c. None of the plants are completed by the contract date.

d. Only the plant at Site 1 is completed by the contract date.

e. Exactly one of the three plants is completed by the contract date.

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