Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Which of the following is NOT a subset of the set {p, o, 7}?
1)
A)
7
B)
{o, 7}
C)
{p, o, 7}
D)
2)
One of the following is false; indicate by letter which one:
2)
A)
4
{3, 4, 5, 6}
B)
5
{3, 4, 5, 6}
C)
{4}
{3, 4, 5, 6}
D)
4
{3, 4, 5, 6}
3)
A combination lock on a suitcase has 5 wheels, each labeled with digits 1 to 8. How many
5–digit combination lock codes are possible if no digit can be repeated?
3)
4)
A person purchasing a new car has several options: 6 interior color choices, 5 exterior color
choices, 2 choices of radios, and 5 choices of body styles. How many different cars are
possible if one choice is made for each option?
4)
5)
Construct a truth table for the proposition and determine whether it is a contingency, a
tautology, or a contradiction: ~p
q.
5)
6)
How many different five–letter code words are possible from the first ten letters of the
alphabet if the first letter cannot be a vowel and adjacent letters must be different.
6)
7)
A coin that can turn up either heads (H) or tails (T) is flipped. If a head turns up on the first
toss, a spinner that can land on any of the first 7 natural numbers is spun. If a tail turns up,
the coin is flipped a second time. What are the different possible outcomes?
7)
8)
Let U = {a, l, i, t, e}, A = {l, i, t},B = {l, e}, C = {a, l, i, t, e}, and D = {a, e}. Find (C B) A .
8)
9)
Construct a truth table to determine whether or not the following implication is true:
~(p
q) ~p ~q.
9)
10)
State the converse and contrapositive of the position, “If n is an integer that is a multiple of
15, then n is an integer that is a multiple of 3 and a multiple of 5.”
10)
11)
A test is composed of 4 multiple choice problems and 8 questions that can be answered
true or false. Each multiple choice problem has 4 choices. How many different response
sheets are possible if only one choice is marked for each question?
11)
12)
How many nine–digit ZIP code numbers are possible if the first digit cannot be a four and
adjacent digits cannot be the same?
12)
13)
In a marketing survey involving 1,000 randomly chosen people, it is found that 660 use
brand P, 440 use brand Q, and 220 use both brands. How many people in the survey use
brand P and not brand Q?
13)
14)
Construct a truth table for the proposition and determine whether it is a contingency, a
tautology, or a contradiction: (q
p) ~q.
14)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a truth table for the proposition.
15)
~p
(~p
s)
15)
A)
p s ~p
(~p
s)
T T T
T F T
F T T
F F T
B)
p s ~p
(~p
s)
T T T
T F F
F T T
F F F
C)
p s ~p
(~p
s)
T T F
T F F
F T T
F F F
D)
p s ~p
(~p
s)
T T T
T F T
F T T
F F F
16)
n(A)
16)
A)
12
B)
9
C)
17
D)
4
17)
If the police have 9 suspects, how many different ways can they select 5 for a lineup?
17)
A)
126
B)
3024
C)
15,120
D)
45
18)
In a group of 42 students, 22 take history, 17 take biology and 8 take both history and biology.
How many students take biology, but not history?
18)
A)
22
B)
17
C)
9
D)
5
19)
A Super Duper Jean company has 3 designs that can be made with short or long length. There are 5
color patterns available. How many different types of jeans are available from this company?
19)
A)
8
B)
25
C)
15
D)
10
E)
30
20)
Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans,
and 17 like both red and green jelly beans. How many of the students surveyed like no green jelly
beans?
20)
A)
30
B)
38
C)
21
D)
17
21)
A pollster wants to minimize the effect the order of the questions has on a person’s response to a
survey. How many different surveys are required to cover all possible arrangements if there are 6
questions on the survey?
21)
A)
6
B)
120
C)
36
D)
720
22)
At Southern States University (SSU) there are 399 students taking Finite Mathematics or Statistics.
238 are taking Finite Mathematics, 184 are taking Statistics, and 23 are taking both Finite
Mathematics and Statistics. How many are taking Finite Mathematics but not Statistics?
22)
A)
215
B)
192
C)
376
D)
161
23)
2! 2!
23)
A)
1
B)
4
C)
12
D)
6
24)
A home cooking equipment supply company employs 7 sales representatives and 6 product
designers. How many ways can this company select 4 of these employees to send to a product
demonstration convention in Oahu if at least 3 product designers must attend?
24)
A)
504
B)
155
C)
168
D)
42
25)
In Virginia, each automobile license plate consists of a single digit followed by three letters,
followed by three digits. How many distinct license plates can be formed if there are no restrictions
on the digits or letters?
25)
A)
10,757,600
B)
17,576
C)
175,7560,000
D)
175,760
E)
17,575,600
26)
p ~q
26)
A)
p q p ~q
T T T
T F F
F T T
F F T
B)
p q p ~q
T T F
T F T
F T T
F F T
C)
p q p ~q
T T T
T F T
F T F
F F F
D)
p q p ~q
T T F
T F F
F T T
F F T
27)
n(A) = 33, n(B) = 15, n(A B) = 42, n(B’) = 40. Find n(A
B)’.
27)
A)
49
B)
13
C)
36
D)
42
28)
B E
28)
A)
finite
B)
infinite
29)
~p ~q
29)
A)
p q (~p ~q)
T T F
T F F
F T F
F F F
B)
p q (~p ~q)
T T F
T F F
F T F
F F T
C)
p q (~p ~q)
T T F
T F T
F T T
F F T
D)
p q (~p ~q)
T T T
T F F
F T F
F F T
30)
{all odd integers greater than –3 and less than 5} = {–1, 1, 3}
30)
A)
True
B)
False
Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement
is true or false.
31)
U
A
31)
A)
True
B)
False
Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.
32)
{3, 0, 8}
A
32)
A)
True
B)
False
Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n
N| n > 50}
B = {n
N| n < 250}
O = {n
N| n is odd}
E = {n
N| n is even}
33)
A’
33)
A)
infinite
B)
finite
B)
Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set,
and let
A = {n
N| n > 50}
B = {n
N| n < 250}
O = {n
N| n is odd}
E = {n
N| n is even}
34)
O
E’
34)
A)
disjoint
B)
not disjoint
B)
35)
C7, 0
35)
A)
1
B)
7
C)
720
D)
6
B)
36)
7
{14, 21, 28, 35, 42}
36)
A)
True
B)
False
B)
37)
10!
37)
A)
362,880
B)
7,257,600
C)
3,628,800
D)
1,814,400
B)
Use the Venn diagram below to find the number of elements in the region.
38)
n(A B)
38)
A)
21
B)
11
C)
29
D)
14
39)
Suppose there are 4 trains connecting town X to town Y and 6 roads connecting town Y to town Z.
In how many ways can a person travel from X to Z via Y?
39)
A)
12
B)
36
C)
10
D)
24
E)
16
Evaluate.
40)
13!
12!
40)
A)
12
B)
6
C)
26
D)
13
Express the proposition as an English sentence and determine whether it is true or false, where p and q are the
propositions
p: “9 · 9 = 81″ q: “8 · 10 < 7 · 11
41)
p
q
41)
A)
8 · 10 is not less than 7 · 11; true
B)
9 · 9 = 81 and 8 · 10 < 7 · 11; false
C)
9 · 9 = 81 or 8 · 10 < 7 · 11; true
D)
If 9 · 9 = 81, then 8 · 10 < 7 · 11; false
Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
42)
n(A) = 33, n(B) = 19, n(A
B) = 1, n(A’
B’) =9. Find n(U).
42)
A)
64
B)
60
C)
51
D)
52
Determine whether the selection is a permutation, a combination, or neither.
43)
Mary baked 3 pies: 1 for her father, 1 for her friend Joe, and 1 for her coworkers.
43)
A)
combination
B)
permutation
C)
neither
44)
A local television station sends out questionnaires to determine if viewers would rather see a
documentary, an interview show, or reruns of a game show. There were 950 responses with the
following results:
285 were interested in an interview show and a documentary, but not reruns.
38 were interested in an interview show and reruns but not a documentary
133 were interested in reruns but not an interview show.
228 were interested in an interview show but not a documentary.
95 were interested in a documentary and reruns.
57 were interested in an interview show and reruns.
76 were interested in none of the three.
How many are interested in exactly one kind of show?
44)
A)
466
B)
436
C)
456
D)
446
45)
In a Power Ball lottery, 5 numbers between 1 and 12 inclusive are drawn. These are the winning
numbers. How many different selections are possible? Assume that the order in which the numbers
are drawn is not important.
45)
A)
248,832
B)
792
C)
120
D)
95,040
46)
How many 4–digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is
not allowed?
46)
A)
23
B)
2401
C)
24
D)
840
Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement
is true or false.
47)
A
A
47)
A)
True
B)
False
48)
A restaurant offered pizza with 3 types of crusts and 7 different toppings. How many different
types of pizzas could be offered?
48)
A)
21
B)
49
C)
10
D)
63
E)
9
49)
How many ways can a committee of 4 be selected from a club with 10 members?
49)
A)
10,000
B)
5040
C)
210
D)
40
50)
In a group of 42 students, 22 take history, 17 take biology and 8 take both history and biology.
How many students take neither biology nor history?
50)
A)
22
B)
5
C)
8
D)
11
Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n
N| n > 50}
B = {n
N| n < 250}
O = {n
N| n is odd}
E = {n
N| n is even}
51)
A
O’
51)
A)
finite
B)
infinite
52)
Find A.
8 x q
5
3 g
52)
A)
{8, 3, 5}
B)
{5}
C)
{5, x, q, g}
D)
{8, 3, 5, x}
Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set,
and let
A = {n
N| n > 50}
B = {n
N| n < 250}
O = {n
N| n is odd}
E = {n
N| n is even}
53)
A’
B’
53)
A)
not disjoint
B)
disjoint
54)
A survey of residents in a certain town indicates 170 own a dehumidifier, 130 own a snow blower,
and 80 own a dehumidifier and a snow blower. How many own a dehumidifier or a snow blower?
54)
A)
170
B)
250
C)
80
D)
220