Deck 7: Multivariable Calculus

Question 1

Tell whether the statement is true or false.
{all odd integers greater than -3 and less than 5} = {-1, 1, 3}

Answer 1

True

Question 2

Provide an appropriate response.
Construct a truth table to determine whether or not the following implication is true: is true:

Answer 2

Question 3

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

A) 9 · 9 = 81 and 8 · 10 < 7 · 11; false
B) If 9 · 9 = 81, then 8 · 10 < 7 · 11; false
C) 8 · 10 is not less than 7 · 11; true
D) 9 · 9 = 81 or 8 · 10 < 7 · 11; true

Answer 3

9 · 9 = 81 and 8 · 10 < 7 · 11; false

Question 4

Tell whether the statement is true or false.

Question 5

Construct a truth table for the proposition.

A)
B)
C)
D)

Question 6

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
The contrapositive of he contrapositive of

A) If 8 · 10 is not less than 7 · 11, then 9 · 9 is equal to 81; false
B) If 8 · 10 is less than 7 · 11, then 9 · 9 is equal to 81; false
C) If 8 · 10 is not less than 7 · 11, then 9 · 9 is not equal to 81; false
D) If 8 · 10 is less than 7 · 11, then 9 · 9 is not equal to 81; false

Question 7

Construct a truth table to decide if the two statements are equivalent.

Question 8

Construct a truth table to decide if the two statements are equivalent.

Question 9

Provide an appropriate response.
Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a
contradiction: (q p ) ) ~q.

Question 10

Provide an appropriate response.
Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a
contradiction:

Question 11

Provide an appropriate response.
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."

Question 12

Construct a truth table for the proposition.

A)
B)
C)
D)

Question 13

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.

Question 14

Construct a truth table for the proposition.

A)
B)
C)
D)

Question 15

Tell whether the statement is true or false.

Question 16

Construct a truth table to decide if the two statements are equivalent.

Question 17

Construct a truth table for the proposition.

A)
B)
C)
D)

Question 18

Tell whether the statement is true or false.

Question 19

Construct a truth table to decide if the two statements are equivalent.

Question 20

Construct a truth table to decide if the two statements are equivalent.
~

Question 21

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) not disjoint
B) disjoint

Question 22

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.

Question 23

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.

Question 24

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.

Question 25

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
n(A) = 33, n(B) = 15, 15, = 42, n(B') = 40. Find

A) 36
B) 42
C) 49
D) 13

Question 26

Use the Venn diagram to find the requested set.
Find B.

A) {a, b, g, j, q, n, w}
B) {a, b, g, j, n, w}
C) {b, g}
D) {q}

Question 27

Use the Venn diagram to find the requested set.
Find

A) {8, 3, 4, z, r, f}
B) {4}
C) {8}
D)

Question 28

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.

Question 29

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
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

Question 30

Use the Venn diagram to find the requested set.
Find A.

A) {5}
B)
C)
D)

Question 31

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.

Question 32

Use the Venn diagram to find the requested set.
Find

A) {d, c, g, i, m, w}
B) {d, c, g, i, q, m, w}
C) {q}
D) {c, g}

Question 33

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.

Question 34

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.

Question 35

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
n(A) = 33, n(B) = 19, 19, n(A

A) 60
B) 64
C) 51
D) 52

Question 36

Provide an appropriate response.
One of the following is false; indicate by letter which one:

A)
B)
C)
D)

Question 37

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let

A) finite
B) infinite

Question 38

Provide an appropriate response.
Which of the following is NOT a subset of the set owing is NOT a subset of the set {p, o,

A) 7
B)
C)
D)

Question 39

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let

A) infinite
B) finite

Question 40

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let

A) finite
B) infinite

Question 41

Provide an appropriate response.
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?

A) 22
B) 5
C) 17
D) 9

Question 42

Provide an appropriate response.
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 neither red nor green jelly beans?

A) 13
B) 12
C) 8
D) 17

Question 43

Provide an appropriate response.
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?

A) 80
B) 250
C) 170
D) 220

Question 44

Provide an appropriate response.
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?

A) 8
B) 5
C) 11
D) 22

Question 45

Use the Venn diagram below to find the number of elements in the region.
n(A)

A) 9
B) 12
C) 4
D) 17

Question 46

Use the Venn diagram below to find the number of elements in the region.

A) 29
B) 21
C) 11
D) 14

Question 47

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) not disjoint
B) disjoint

Question 48

Use the addition principle for counting to solve the problem.
If n(B) = 24, n 24, n =5, and n, and n = 42, find n(A).

A) 24
B) 25
C) 23
D) 21

Question 49

Use the Venn diagram below to find the number of elements in the region.

A) 29
B) 14
C) 24
D) 39

Question 50

Use the Venn diagram below to find the number of elements in the region.

A) 44
B) 8
C) 16
D) 18

Question 51

Provide an appropriate response.
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 500 responses with the following results:
150 were interested in an interview show and a documentary, but not reruns.
20 were interested in an interview show and reruns but not a documentary
70 were interested in reruns but not an interview show.
120 were interested in an interview show but not a documentary.
50 were interested in a documentary and reruns.
30 were interested in an interview show and reruns.
40 were interested in none of the three.
How many are interested in exactly one kind of show?

A) 230
B) 220
C) 250
D) 240

Question 52

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
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?

A) 192
B) 215
C) 376
D) 161

Question 53

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
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

Question 54

Provide an appropriate response.
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 only a dog?

A) 10
B) 22
C) 15
D) 18

Question 55

Use the addition principle for counting to solve the problem.
If n(A) = 20, n 20, n = 58, and n = 16, find n(B).

A) 54
B) 53
C) 55
D) 58

Question 56

Use the addition principle for counting to solve the problem.
If n(A) = 40, n(B) = 117 and d = 137, what is

A) 40
B) 10
C) 22
D) 20

Question 57

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
At Southern States University SSU) there are 719 students taking Finite Mathematics or Statistics. 328 are taking Finite Mathematics, 476 are taking Statistics, and 85 are taking both Finite Mathematics and Statistics. How
Many are taking Statistics but not Finite Mathematics?

A) 243
B) 391
C) 158
D) 634

Question 58

Use the addition principle for counting to solve the problem.
If n(A) = 5, n(B) = 11 and 11 and

A) 14
B) 13
C) 11
D) 12

Question 59

Use the Venn diagram below to find the number of elements in the region.

A) 2
B) 10
C) 18
D) 37

Question 60

Use the Venn diagram below to find the number of elements in the region.

A) 14
B) 11
C) 33
D) 15

Question 61

Provide an appropriate response.
A restaurant offered pizza with 3 types of crusts and 7 different toppings. How many different types of pizzas could be offered?

A) 21
B) 9
C) 49
D) 10
E) 63

Question 62

Evaluate.
P6, 4

A) 360
B) 30
C) 2
D) 24

Question 63

Provide an appropriate response.
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?

Question 64

Provide an appropriate response.
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?

A) 10
B) 16
C) 12
D) 24
E) 36

Question 65

Provide an appropriate response.
How many nine-digit ZIP code numbers are possible if the first digit cannot be a four and adjacent digits
cannot be the same?

Question 66

Provide an appropriate response.
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?

A) 30
B) 10
C) 8
D) 15
E) 25

Question 67

Evaluate.
6!

A) 1440
B) 120
C) 720
D) 360

Question 68

Provide an appropriate response.
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?

A) 17,575,600
B) 175,7560,000
C) 17,576
D) 175,760
E) 10,757,600

Question 69

Provide an appropriate response.
License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?

A) 308,915,776
B) 1,757,600
C) 1,000,000
D) 175,760
E) 17,576,000

Question 70

Provide an appropriate response.
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?

Question 71

Evaluate.
P10, 2

A) 90
B) 45
C) 8
D) 19

Question 72

Evaluate.
1514!!

A) 7
B) 30
C) 14
D) 15

Question 73

Provide an appropriate response.
The access code to a house's security system consists of five digits. How many different codes are available if each digit can be repeated?

A) 32
B) 45
C) 5
D) 100,000
E) 3125

Question 74

Provide an appropriate response.
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.

Question 75

Provide an appropriate response.
How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of digits is allowed.

A) 5000
B) 2999
C) 1512
D) 2997
E) 2000

Question 76

Evaluate.

A) 7
B) 1
C) 42
D) 21

Question 77

Evaluate.
86!!

A)-86
B) 2!
C) 56
D) 8

Question 78

Evaluate.

A) 720
B) 28
C) 1440
D) 4

Question 79

Provide an appropriate response.
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?

Question 80

Provide an appropriate response.
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?