Question

a survey of 65 customers was taken at a bookstore regarding the types of books purchased. the survey found that 39 customers purchased mysteries, 31 purchased science fiction, 24 purchased romance novels, 17 purchased mysteries and science fiction, 13 purchased mysteries and romance novels, 10 purchased science fiction and romance novels, and 6 purchased all three types of books.
a) how many of the customers surveyed purchased only science fiction?
b) how many purchased mysteries and science fiction, but not romance novels?
c) how many purchased mysteries or science fiction?
d) how many purchased mysteries or science fiction, but not romance novels?
e) how many purchased exactly two types of books?

a) there were 10 customers who purchased only science fiction
(simplify your answer.)
b) there were 11 customers who purchased mysteries and science fiction, but not romance novels.
(simplify your answer.)
c) there were \\(\square\\) customers who purchased mysteries or science fiction.
(simplify your answer.)

Explanation:

Step1: Recall the principle of inclusion - exclusion for two sets.

The formula for \(|M \cup S|\) (where \(M\) is the set of customers who purchased mysteries and \(S\) is the set of customers who purchased science fiction) is \(|M|+|S|-|M\cap S|\).
We know that \(|M| = 39\), \(|S|=31\) and \(|M\cap S| = 17\).

Step2: Substitute the values into the formula.

\(|M\cup S|=39 + 31-17\)
First, calculate \(39+31=70\), then \(70 - 17=53\).

Answer:

53