MA 114-001, Fall 2014 — Test 3 Review
Note that all work must be shown (or explained, as the case may be) to guarantee full credit.
Also, keep all numbers as fractions when necessary (i.e. when dividing 1 by 3, 2 by 7, etc.) and
simplify fractions as much as possible.
1. ( Points) For each given set, draw a two-circle Venn diagram and shade the portion corresponding
to it.
(a) (
S
0
\
T
)
[
(
S
\
T
)
(b) (
S
\
T
0
)
[
(
S
0
[
T
)
(c)
S
0
\
T
0
2. ( Points)
For each given set, draw a three-circle Venn diagram and shade the portion corre-
sponding to it.
(a) (
R
\
S
\
T
)
0
(b)
R
\
(
S
[
T
)
(c) (
R
\
T
0
)
[
(
S
\
T
)
3. ( Points)
A merchant surveed 400 people to determine from what source they found out about
a sale. The results of the survey are:
180 from the Internet
190 from television
190 from newspapers
80 from the Internet and television
90 from the Internet and newspapers
50 from television and newspapers
30 from all sources
(a) Draw a Venn diagram that represents the given data and determine the number in each
basic region.
(b) How many people learned of the sale from newspapers or the Internet?
(c) How many people learned of the sale only from newspapers?
(d) How many people learned of the sale from the Internet or television but not newspapers?
(e) How many people learned of the sale from at least two of the three media?
(f) How many people learned of the sale from exactly one of the three media?
4. ( Points) Let
R
,
S
, and
T
be subsets of the universal set
U
. Let
n
(
U
) = 64,
n
(
R
[
S
[
T
) = 45,
n
(
R
) = 22,
n
(
T
) = 26,
n
(
R
\
S
) = 4,
n
(
S
\
T
) = 6,
n
(
R
\
T
) = 8, and
n
(
R
\
S
\
T
) = 1. Draw
an appropriate Venn diagram and use the given data to determine the number fo elements in each
basic region.
5. ( Points)
A particular bridge association has 3200 sanctioned clubs. Each club holds 2 games

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