Answer to Question #287850 in Discrete Mathematics for Christar

Question

In a survey of 130 people, the following data were collected: 106 people subscribed to the newspaper, 29

people subscribed to magazines, and 17 people were members of a mail CD club. Seventeen subscribed to

both the newspaper and the magazines, 5 people subscribed to magazines and were members of a CD

club, and 10 people subscribed to the newspaper and were members of a mail CD club. Three people

subscribed to both the newspaper and magazines and were members of a mail CD club. Make and fill in a

Venn diagram to illustrate this situation

Answer 1

Solution:

Let A= people subscribed to the newspaper

B= people subscribed to magazines

C= people were members of a mail CD club.

$\therefore n(A)=106 \\n(B)=29 \\n(C)=17$

$n(A \cap B)=17$ (both newspaper and magazines)

$n(B \cap C)=5$ (both magazine and member of CD club)

$n(C \cap A)=10$ (both newspaper and member of CD club)

$n(A \cap B \cap C)=3$ (both magazine, newspaper and

$n(A \cup B \cup C)=130$