MATH FOR LIBERAL ARTS
REVIEW 1
L F Thomas - Instructor
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Fill in the blank with either or to make the statement
true.
8) Saskatchewan _____ the set of states in the
United States
Write a word description of the set.
1) {10, 12, 14, 16, ..., 100}
9) 72,544 _____ the set of even natural numbers
List the elements in the set.
2) The set of the days of the week
Express the set using the roster method.
10) {x | x N and x lies between 2 and 6}
The line graph shows the percentage of obese young
adults in a certain city over time. Based on the information
in the graph, represent the set using the roster method.
3)
11) the set of natural numbers less than or equal to
11
Express the set using set-builder notation. Use inequality
notation to express the consition x must meet in order to
be a member of the set.
12) A = {18, 19, 20, 21, 22,...}
30
25
20
Find the cardinal number for the set.
13) {27, 29, 31, 33, 35}
15
Are the sets equivalent?
14) A = {Larry, Moe, Curly. Shemp}
B = {Posh, Sporty, Baby, Scary}
10
5
15) A = {13, 14, 14, 15, 15, 15, 16, 16, 16, 16}
B = {16, 15, 14, 13}
{x | x is a year in which 20% of young
Americans in city X are obese}
Determine whether the set is finite or infinite.
16) {x | x N and x 100}
Determine if the set is the empty set.
4) {0, }
17) {x | x N and x 1000}
Are the sets equal?
18) {e, f, g, h} = {f, h, g, e}
5) {x|x < 12 and x > 16}
6) {x|x
and 2 < x < 6}
Write
true.
Determine whether the statement is true or false.
7) 4 {1, 2, 3, ..., 15}
or
in the blank so that the resulting statement is
19) {4, 34, 39}
{15, 34, 39, 49}
20) {c, a, n, d, i, d, a, t, e} _____ {a, c, d, e, i, t, a, n,
d}
1
Use , , , or both and to make a true statement.
21) {a, b} {z, a, y, b, x, c}
Use the Venn diagram to list the elements of the set in
roster form.
30)
Use the formula for the number of subsets of a set with n
elements to solve the problem.
22) A village has 4 fire engines. If a radio
dispatcher receives a call, depending on the
nature of the situation, no engines, one engine,
two engines, three engines, or all four engines
can be sent to a fire. How many options does
the dispatcher have for sending the fire
engines to the scene of the caller?
A B
Use the Venn diagram to list the elements of the set in
roster form.
31)
A B
32)
23) The set of students who studied Saturday
24) The set of students who studied Saturday and
Sunday
Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to
write the complement of the set.
25) A = {2, 4, b, d}
(A B)'
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
26) A B'
33)
27) (A B)'
28) A B
A' B
29) (A B)'
2
Provide an appropriate response.
refers to the union of sets;
34) The word
the word
Use the Fundamental Counting Principle to solve the
problem.
43) There are 7 performers who are to present their
acts at a variety show. One of them insists on
being the first act of the evening. If this request
is granted, how many different ways are there
to schedule the appearances?
refers to the intersection of
sets.
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
35) A (B C)
Evaluate the factorial expression.
5!
44)
3!
36) A (B C)
45) (9 - 5)!
37) (A B) (A C)
Use the formula for nPr to solve.
46) In a contest in which 8 contestants are entered,
in how many ways can the 5 distinct prizes be
awarded?
Use the Venn diagram shown to answer the question.
47) A church has 10 bells in its bell tower. Before
each church service 3 bells are rung in
sequence. No bell is rung more than once. How
many sequences are there?
48) A club elects a president, vice-president, and
secretary-treasurer. How many sets of officers
are possible if there are 13 members and any
member can be elected to each position? No
person can hold more than one office.
Solve the problem.
49) In how many distinct ways can the letters in
IMMUNOLOGY be arranged?
38) Which regions represent set D F?
50) In how many distinct ways can the letters in
ENGINEERING be arranged?
39) Which regions represent set D E?
40) Which regions represent set E'?
Solve the problem by applying the Fundamental Counting
Principle with two groups of items.
41) In how many ways can a girl choose a
two-piece outfit from 5 blouses and 6 skirts?
42) A restaurant offers a choice of 4 salads, 5 main
courses, and 4 desserts. How many possible
3-course meals are there?
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Answer Key
Testname: SPRING 2015 REVIEW1
1) even numbers from 10 to 100
2) {Friday, Monday, Saturday, Sunday, Thursday,
Tuesday, Wednesday}
3) {1990}
4) No, it is not the empty set.
5) Yes, it is the empty set.
6) No, it is not the empty set.
7) True
8)
9)
10) {3, 4, 5}
11) {1, 2, 3, . . . , 11}
12) {x | x N and x 18}
13) 5
14) Yes
15) No
16) Finite
17) Infinite
18) Yes
19)
20)
21) and
22) 16
23) {Karen, Charly, Sam, Sophia}
24) {Sam, Sophia}
25) {1, 5, a, c, e}
26) {u, w}
27) {r, t, u, v, w, x, z}
28) {q, s, y}
29) {r, t, v, x}
30) {11, 12, 13, 14, 15, 16, 17}
31) {13, 17}
32) {11, 12, 14, 15, 16, 18, 19}
33) {12, 15, 16}
34) or; and
35) {q, s, u, w, y, z}
36) {q, s, w, y}
37) {q, s, u, w, y, z}
38) I, II, IV, V, VI, VII
39) II, V
40) I, IV, VII, VIII
41) 30
42) 80
43) 720
44) 20
45) 24
46) 6720
47) 720
48) 1716
49) 907,200
4
Answer Key
Testname: SPRING 2015 REVIEW1
50) 277,200
5