Problem 105SE

Survey on energy conservation. A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting and reviewing one of the returned questionnaires. Consider the events: A: {The home is constructed of brick.} B: {The home is more than 30 years old.} C: {The home is heated with oil.} Describe each of the following events in terms of unions, intersections, and complements (i.e., A ∪ B, A∩B, Ac, etc.):

a. The home is more than 30 years old and is heated with oil.

b. The home is not constructed of brick.

c. The home is heated with oil or is more than 30 years old.

d. The home is constructed of brick and is not heated with oil.

Solution

Step 1 of 4:

Let A, B, and C be the three events.

A: {The home ic constructed of brick}.

B: {The home more than 30 years old}.

C: {The home is heated with oil}.

Our goal is:

We need to describe each of the following events in terms of unions, intersections, and complements.

Now we have to describe each of the following events in terms of unions, intersections, and complements.

a).

Given the home is more than 30 years old is heated with oil.

Hence BA.