Question

It was once said that Country-Western songs emphasize
three basic themes: love, prison, and trucks. A survey of the local Country-
Western radio station produced the following data:
12 songs about a truck driver who is in love while in prison
13 about a prisoner in love
28 about a person in love
18 about a truck driver in love
3 about a truck driver in prison who is not in love
2 about people in prison who are not in love and do not drive trucks
8 about people who are out of prison, are not in love, and do not drive trucks
16 about truck drivers who are not in prison
(a) How many songs were surveyed?
Find the number of songs about:
(b) truck drivers
(c) prisoners
(d) truck drivers in prison
(e) people not in prison
(f) people not in love

Answer 1

Consider that country-western songs emphasize three basic themes: love, prison, and trucks. A survey of the local country-western radio station produced the following data:

Songs about a truck driver, who is in love while in prison

About a prisoner in love

About a person in love

About a truck-driver in love

About a truck-driver in prison, who is not in love

About people in prison, who are not in love and do not drive trucks

About people who are out of prison, are not in love and do not drive trucks

About truck drivers who are not in prison

Consider the following Venn diagram:

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According to the Venn diagram and above data: Substitutein the equation, therefore,

Substitutein the equation, therefore,

Substitute in the equation,

And substitutein the equation,

And from the figure it is clear that,

Substitute in the equation,

(a)

The number of songs surveyed is

Hence, the number of songs surveyed is:

(b)

The number of songs about truck drivers is

Hence, the number of songs about truck drivers is:

(c)

The number of songs about prisoners is

Hence, the number of songs about prisoners is:

(d)

The number of songs about truck drivers in prison is

Hence, the number of songs about truck drivers in prison is:

(e)

The number of songs about people not in prison is

Hence, the number of songs about people not in prison is:

(f)

The number of songs about people not in love is

Hence, the number of songs about people not in love is: