Question

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 one of the returned questionnaires. Consider the events:

A: {The home is constructed of brick}
B: {The home is more than 30 years old}
In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old.
A ∩ Bc
A ∩ B
(A ∩ B)c
A ∪ B

Answer 1

A home that is constructed of brick and is less than or equal to 30 years old can be described as the intersection of A and B (A ∩ B).

Step-by-step explanation:

In terms of events A (the home is constructed of brick) and B (the home is more than 30 years old), a home that is constructed of brick and is less than or equal to 30 years old can be described as the intersection of A and B, denoted as A ∩ B.

So, the event A ∩ B represents the set of homes that are both constructed of brick and are more than 30 years old.

Answer 2

A ∩ Bc

Step-by-step explanation:

Home constructed of brick:

Event A

Home is less than or equal to 30 years old.

Event B is: {The home is more than 30 years old}

So the event home is less than or equal to 30 years old is the negation(complement) of B. So Bc.

And:

And means intersection.

We have the intersection of events A and the complement of event B, which is represented by:

A ∩ Bc