Test One Review
MATH 1332 Math for Liberal Arts
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write a word description of the set.
1) {January, February, March, April, May, June, July, August, September, October,
November, December}
Express the set using the roster method.
2) The set of the days of the week.
1)
2)
The line graph shows the percentage of obese adults in a certain city by age. Based on the information in the graph,
represent the set using the roster method.
3)
3)
30
25
20
15
10
5
{x | x is an age at which 20% of adults in city X are obese}
Determine if the set is the empty set.
4) {x|x is a day of the week whose name begins with the letter Y}
5) {∅}
4)
5)
Determine whether the statement is true or false.
6) 15 ∈ {2, 4, 6, ..., 20}
6)
Fill in the blank with either ∈ or ∉ to make the statement true.
7) 0 _____ ∅
7)
1
Express the set using the roster method.
8) {x | x ∈ N and x is greater than 13}
8)
Express the set using set-builder notation. Use inequality notation to express the condition x must meet in order to be a
member of the set.
9) A = {800, 801, 802, . . ., 8000}
9)
Find the cardinal number for the set.
10) {27, 29, 31, 33, 35}
10)
11) {x | x is a day of the week that begins with the letter N}
Are the sets equivalent?
12) A = {11, 13, 15, 17, 19}
B = {12, 14, 16, 18, 20}
11)
12)
Determine whether the set is finite or infinite.
13) The set of natural numbers less than 100
13)
14) {x | x ∈ N and x ≥ 1000}
14)
Are the sets equal?
15) A = {16, 17, 17, 18, 18, 18, 19, 19, 19, 19}
B = {19, 18, 17, 16}
15)
Write ⊆ or ⊈ in the blank so that the resulting statement is true.
16) {x | x is a tree} _____ {x | x is a birch tree}
16)
Determine whether the statement is true or false.
17) Ted ⊆ {Bob, Carol, Ted, Alice}
17)
18) {Carol} ⊆ {Bob, Carol, Ted, Alice}
18)
19) ∅ ⊆ {France, Germany, Switzerland}
19)
Use ⊆ , ⊈ , ⊂ , or both ⊂ and ⊆ to make a true statement.
20) {a, b} {z, a, y, b, x, c}
20)
2
21) {4, 5, 6}
{4, 5, 6}
21)
22) {x | x is a male who is registered with Selective Service} _____ {x | x is a male who is in the
Army}
List all the subsets of the given set.
23) {Siamese, domestic shorthair}
22)
23)
24) ∅
24)
Use the formula for the number of subsets of a set with n elements to solve the problem.
25) 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?
25)
Use the Venn diagram to list the elements of the set in roster form.
26) The set of students who studied neither Saturday nor Sunday
26)
Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set.
27) Q = {2, 4, b, d}
27)
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.
28) (A ∩ B)'
28)
3
Use sets to solve the problem.
29) Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey.
Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5
students own both a cat and a dog. How many of the students surveyed own
neither a cat nor a dog?
Provide an appropriate response.
30) The word
refers to the union of sets; the word
refers to the intersection of
29)
30)
sets.
Use the formula for the cardinal number of the union of two sets to solve the problem.
31) Set A contains 9 letters and 9 numbers. Set B contains 12 letters and 9 numbers. Three
letters and 2 numbers are common to both sets A and B. Find the number of elements in set
A or set B.
Determine whether the sentence is a statement.
32) The orbit of Pluto lies completely within the orbit of Uranus.
33) Does she always act like that when she's unhappy?
Provide an appropriate response.
34) In symbolic logic, we use
31)
32)
33)
to represent statements.
Form the negation of the statement.
35) Today is June 19
34)
35)
36) Copenhagen is not the capital of Brazil.
36)
Let p, q, r, and s represent the following statements:
p: One plays hard.
q: One is a guitar player.
r: The commute to work is not long.
s: It is not true that the car is working.
Express the following statement symbolically.
37) One does not play hard.
37)
38) The car is working.
38)
4
Express the symbolic statement ~p in words.
39) p: Vitamin C helps the immune system.
39)
40) p: The refrigerator is not working.
40)
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Answer Key
Testname: TEST ONE REVIEW MATH 1332 SPRING 2017
1) months of the year
2) {Friday, Monday, Saturday, Sunday, Thursday,
Tuesday, Wednesday}
3) {50}
4) Yes, it is the empty set.
5) No, it is not the empty set.
6) False
7) ∉
8) {14,15,16,...}
9) {x | x ∈ N and 800 ≤ x ≤ 8000}
10) 5
11) 0
12) Yes
13) Finite
14) Infinite
15) Yes
16) ⊈
17) False
18) True
19) True
20) ⊂ and ⊆
21) ⊆
22) ⊈
23) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { }
24) ∅
25) 16
26) {Vijay}
27) {1, 5, a, c, e}
28) {r, t, u, v, w, x, z}
29) 12
30) or; and
31) 34
32) statement
33) not a statement
34) lowercase letters
35) Today is not June 19.
36) It is not true that Copenhagen is not the capital of Brazil.
37) ~p
38) ~s
39) Vitamin C does not help the immune system.
40) The refrigerator is working.
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