MA 114-002
Test 3
March 16, 2016
Answer the questions in the blue book provided. You must show all of your
work to receive full credit. Only non-graphing calculators are allowed for this
exam.
You may leave your answer as
C
p
n, k
q
for appropriate
n
and
k
.
1.
2 points
In the following questions, indicate whether the statement is true or false. If
it is false, provide a counter-example.
(a)
S
is a subset of
S
Y
T
(b)
S
X
T
is a subset of
T
1
2. In the following problems, draw a three-circle Venn diagram and label the circles
R
,
S
, and
T
. Shade the portion of the diagram corresponding to the given set.
(a)
2 points
R
Y
S
1
Y
T
1
(b)
3 points
R
1
X p
S
Y
T
q
3. Suppose that
S
and
T
are subsets of the universal set
U
.
Draw a two-circle Venn
diagram, and use the use given information to fill in the number of elements in each of
the non-overlapping regions of the diagram.
(a)
2 points
n
p
U
q “
15,
n
p
S
q “
6,
n
p
T
q “
8,
n
p
S
X
T
q “
2
(b)
3 points
n
p
U
q “
75,
n
p
S
q “
15,
n
p
T
q “
25, and
n
p
S
1
X
T
1
q “
40.
4.
2 points

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