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 53 customers who purchased mysteries or science fiction.
(simplify your answer.)
d) there were \\(\square\\) customers who purchased mysteries or science fiction, but not romance novels.
(simplify your answer.)

Explanation:

Step1: Find only mysteries, only science fiction, and their intersection without romance.

• Only mysteries: \( 39 - 17 - 13 + 6 = 15 \) (using principle of inclusion - exclusion: total mysteries minus those with sci - fi, minus those with romance, plus those with both (since subtracted twice)).
• Only science fiction: 10 (from part a).
• Mysteries and science fiction but not romance: 11 (from part b).

Step2: Calculate "mysteries or science fiction, but not romance".

Using the formula for "or" in sets (excluding romance), we add only mysteries, only science fiction, and mysteries and science fiction but not romance.
So, \( 15+10 + 11=36 \).

Answer:

36