Deck 1: Basic Concepts

Question 1

Determine whether the statement is true or false.

- $\{ 1,3,5,7 , \ldots \}$ is the set of odd natural numbers.

Answer 1

True

Question 2

Determine whether the statement is true or false.
Every irrational number is an integer.

Answer 2

False

Question 3

List the set in roster form.

- $A = \{ x \mid - 2 < x < 1 \text { and } x \in I \}$

A) $\left\{ - 1 , - \frac { 1 } { 2 } , 0 \right\}$
B) $\{ - 2 , - 1,0,1 \}$
C) $\{ - 1,0 \}$
D) $\{ \}$

Answer 3

$\{ - 1,0 \}$

Question 4

Determine whether the statement is true or false.
Some real numbers are integers.

Question 5

Determine whether the statement is true or false.
Every integer is an irrational number.

Question 6

Determine whether the statement is true or false.
The set of integers is an infinite set.

Question 7

Determine whether the statement is true or false.
The set of rational numbers is a finite set.

Question 8

Determine whether the statement is true or false.
Some rational numbers are integers.

Question 9

Insert eithernsert either $< \text { or } >$ to to make the statement true.

--53 _____ -70

A) $>$
B) $<$

Question 10

Insert eithernsert either $< \text { or } >$ to to make the statement true.

- $- \frac { 4 } { 5 } ~\_\_\_ - 1$

A) $<$
B) $>$

Question 11

Determine whether the statement is true or false.
Every whole number is a real number.

Question 12

Determine whether the statement is true or false.
The intersection of the set of rational numbers with the set of irrational numbers is the empty set.

Question 13

Determine whether the statement is true or false.
Every rational number is an integer.

Question 14

Insert eithernsert either $< \text { or } >$ to to make the statement true.

--6 _____ 3

A) $>$
B) $<$

Question 15

Insert eithernsert either $< \text { or } >$ to to make the statement true.

-6.2 _____ 6.3

A) $>$
B) $<$

Question 16

Determine whether the statement is true or false.
The union of the set of rational numbers with the set of irrational numbers is the empty set.

Question 17

Determine whether the statement is true or false.

- $\{ \ldots , - 7 , - 5 , - 3 , - 1,1,3,5,7 , \ldots \}$ is the set of odd natural numbers.

Question 18

Determine whether the statement is true or false.
Some rational numbers are irrational.

Question 19

Insert eithernsert either $< \text { or } >$ to to make the statement true.

- $- \frac { 4 } { 9 } ~\_\_\_ - \frac { 3 } { 7 }$

A) $<$
B) $>$

Question 20

List the set in roster form.

- $S = \{ x \mid x \text { is an even integer greater than } 30 \text { and less than or equal to } 36 \}$

A){32, 34, 36}
B){31, 32, 33, 34, 35, 36}
C){30, 31, 32, 33, 34, 35, 36}
D){30, 32, 34, 36}

Question 21

Illustrate the set on a number line.

- $\{ p \mid - 4 \leq p \leq - 3 \}$

A)
B)
C)
D)

Question 22

$\mathbf { Find~ A \cup R ~and A \cap R~ for~ the~ sets~ A~ and~ B}$

- $A = \{ - 3 , - 2 , - 1 \} , B = \{ 0,1,2 \}$

A) $\begin{array} { l } A \cup B = \{ \} \\A \cap B = \{ - 3 , - 2 , - 1,0,2 \}\end{array}$
B) $\begin{array} { l } A \cup B = \{ - 3 , - 2 , - 1,0,2 \} \\A \cap B = \{ \}\end{array}$
C) $\begin{array} { l } A \cup B = \{ \} \\A \cap B = \{ - 3 , - 2 , - 1,0,1,2 \}\end{array}$
D) $\begin{array} { l } A \cup B = \{ - 3 , - 2 , - 1,0,1,2 \} \\A \cap B = \{ \}\end{array}$

Question 23

Illustrate the set on a number line.

- $\{ \mathrm { t } \mid \mathrm { t } \geq 8 \}$

A)
B)
C)
D)

Question 24

Illustrate the set on a number line.

- $\{ \mathrm { y } \mid \mathrm { y } < - 4 \}$

A)
B)
C)
D)

Question 25

Illustrate the set on a number line.

- $\{ x \mid x > - 4 \}$

A)
B)
C)
D)

Question 26

Solve the problem.
The Little Town Dog Club offers a "Puppy Kindergarten" for puppies in their community. In order for a dog to
advance from this introductory class to the first level obedience class, it must consistently demonstrate
knowledge of each of 4 commands. The instructor has the following table in her record book. Let A = the set of dogs who have demonstrated knowledge of Sit/Stay.
Let B = the set of dogs who have demonstrated knowledge of Down/Stay.
Let C = the set of dogs who have demonstrated knowledge of Heel.
Let D = the set of dogs who have demonstrated knowledge of Come.
Give each of the sets A, B, C, and D using roster notation. Determine the set A ∩ B ∩ C ∩ D. Which dogs are ready to
advance to the next level?

Question 27

Illustrate the set on a number line.

- $\{ x \mid - 5 \leq x \leq 0 \text { and } x \in I \}$

A)
B)
C)
D)

Question 28

List the set in roster form.

- $$S = \{ x \mid x \text { is a natural number less than } 5 \}$$

A){1, 2, 3, 4, 5}
B){0, 1, 2, 3, 4, 5}
C){1, 2, 3, 4}
D){0, 1, 2, 3, 4}

Question 29

Express in set builder notation the set of numbers indicated on the number line.

-

A) $\{ x \mid x < 5 \}$
B) $\{ x \mid x \geq 5 \}$
C) $\{ x \mid x > 5 \}$
D) $\{ x \mid x \leq 5 \}$

Question 30

Illustrate the set on a number line.

- $\{ \mathrm { q } \mid \mathrm { q } < \pi \text { and } \mathrm { q } \in \mathrm { N } \}$

A)
B)
C)
D)

Question 31

$\mathbf { Find~ A \cup R ~and A \cap R~ for~ the~ sets~ A~ and~ B}$

- $\mathrm { A } = \{ 1,2,3,4,5 \},$ $B = \{ 2,4,6,8 \}$

A) $\begin{array} { l } A \cup B = \{ 2,4 \} \\A \cap B = \{ 1,2,3,4,5,6,8 \}\end{array}$
B) $\begin{array} { l } A \cup B = \{ 2,4 \} \\A \cap B = \{ 1,2,3,4,5,6,7,8 \}\end{array}$
C) $\begin{array} { l } \mathrm { A } \cup \mathrm { B } = \{ 1,2,3,4,5,6,8 \} \\\mathrm { A } \cap \mathrm { B } = \{ 2,4 \}\end{array}$
D) $\begin{array} { l } A \cup B = \{ 1,2,3,4,5,6,7,8 \} \\A \cap B = \{ 2,4 \}\end{array}$

Question 32

$\mathbf { Find~ A \cup R ~and A \cap R~ for~ the~ sets~ A~ and~ B}$

-A = { $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}$ B = { $\left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}$

A) $\begin{array} { l } A \cup B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\} \\\\A \cap B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}\end{array}$
B) $\begin{array} { l } \mathrm { A } \cup \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\} \\\\\mathrm { A } \cap \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\}\end{array}$
C) $\begin{array} { l } \mathrm { A } \cup \mathrm { B } = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\\\\mathrm { A } \cap \mathrm { B } = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } , \frac { 1 } { 729 } \right\}\end{array}$
D) $\begin{array} { l } A \cup B = \left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \ldots \right\} \\\\A \cap B = \left\{ \frac { 1 } { 9 } , \frac { 1 } { 81 } \right\}\end{array}$

Question 33

List the set in roster form.

- $S = \{ x \mid x \text { is and integer between } 3 \text { and } 4 \}$

A){3}
B){3, 4}
C) $\left\{ \frac { 7 } { 2 } \right\}$
D){ }

Question 34

List the set in roster form.

- $S = \{ x \mid x \text { is a whole number multiple of } 4 \}$

A){1, 4, 8, 12, 16, . . . }
B){0, 4, 8, 12, 16, . . . }
C){4, 8, 12, 16, 20, . . . }
D){8, 12, 16, 20, 24, . . . }

Question 35

Express in set builder notation the set of numbers indicated on the number line.

- A = -4.8

A) $\{ x \mid x > - 4.8 \}$
B) $\{ x \mid x \leq - 4.8 \}$
C) $\{ x \mid x \geq - 4.8 \}$
D) $\{ x \mid x < - 4.8 \}$

Question 36

Illustrate the set on a number line.

- $\{ \mathrm { k } \mid 2 < \mathrm { k } < 6 \}$

A)
B)
C)
D)

Question 37

Express in set builder notation the set of numbers indicated on the number line.

-

A) $\{ x \mid - 2 \leq x \leq 6 \}$
B) $\{ x \mid - 2 < x \leq 6 \}$
C) $\{ x \mid - 2 < x < 6 \}$
D) $\{ x \mid - 2 \leq x < 6 \}$

Question 38

List the set in roster form.

- $S = \{ x \mid x \text { is an integer greater than } - 5 \}$

A){0, 1, 2, 3, 4, 5, . . . }
B){-4, -3, -2, -1, 0, . . . }
C){1, 2, 3, 4, 5, . . . }
D){-5, -4, -3, -2, -1, 0, . . . }

Question 39

Express in set builder notation the set of numbers indicated on the number line.

-

A) $\{ x \mid x \geq - 6 \}$
B) $\{ x \mid x > - 6 \}$
C) $\{ x \mid x < - 6 \}$
D) $\{ x \mid x \leq - 6 \}$

Question 40

Solve the problem.

-The table shows the students who had a score of 80 or higher on the first two tests in a chemistry class. (Note: Every student in the class had a different first name.) $$\begin{array} { c | c } \begin{array} { c c } \text { First } \\\text { Test }\end{array} & \begin{array} { c } \text { Second } \\\text { Test }\end{array} \\\hline \text { Fred } & \text { Linda } \\\text { Sue } & \text { Earl } \\\text { Ken } & \text { Eloise } \\\text { Eloise } & \text { Fred } \\\text { Roger } & \text { Ken } \\\text { Bill } & \\\text { Cal } &\end{array}$$ Find the set of students who had a score of 80 or higher on the first or second tests.

A){Linda, Ken, Eloise, Roger }
B){Fred, Ken, Eloise}
C){Linda, Sue, Earl, Roger, Bill, Cal}
D){Fred, Linda, Sue, Earl, Ken, Eloise, Roger, Bill, Cal}

Question 41

Evaluate the absolute value expression.

- $| - 4 |$

A)-4
B)0
C)8
D)4

Question 42

Solve the problem.

-List the elements of S that are integers.

A){-5, 0, 3}
B){3}
C) $\left\{ - 5.27 , - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$
D){0, 3}

Question 43

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is Q a subset of I?

A)Yes
B)No

Question 44

Evaluate the absolute value expression.

- $\left| - \frac { 17 } { 22 } \right|$

A)0
B) $\frac { 17 } { 22 }$
C) $\frac { 17 } { 11 }$
D) $- \frac { 17 } { 22 }$

Question 45

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is I a subset of Q?

A)Yes
B)No

Question 46

Evaluate the absolute value expression.

- $\left|\frac { 4 } { 11 }\right|$

A) $\frac { 4 } { 11 }$
B) $- \frac { 4 } { 11 }$
C)0
D) $\frac { 8 } { 11 }$

Question 47

Solve the problem.

-List the elements of S that are real numbers.

A){-5, 0, 3}
B) $\left\{ - 5.27 , - 5,0 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , \sqrt { 3 } , 3 , \sqrt { 12 } \right\}$
C) $\{ \sqrt { 3 } , \sqrt { 12 } \}$
D) $\left\{ - 5.27 , - 5,0 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$

Question 48

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is Q a subset of R?

A)Yes
B)No

Question 49

Solve the problem.

-From the Venn diagram, determine the set A.

A){5, 7}
B){2, 3, 4, 5, 7}
C){2, 3, 4}
D){2, 3, 4, 5, 6, 7, 9}

Question 50

Solve the problem.

-List the elements of S that are rational numbers.

A) $\left\{ - 5.27 , - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$
B){-5, 0, 3}
C) $\left\{ - 5.27 , - 5,0 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , \sqrt { 3 } , 3 , \sqrt { 12 } \right\}$
D) $\left\{ - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$

Question 51

Solve the problem.

-List the elements of S that are whole numbers.

A) $\left\{ - 5.27 , - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$
B){-5, 0, 3}
C){0, 3}
D){3}

Question 52

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is H a subset of R?

A)Yes
B)No

Question 53

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is Q a subset of H?

A)Yes
B)No

Question 54

Evaluate the absolute value expression.

-| $| - 23.5 |$

A)47
B)23.5
C)-23.5
D)0

Question 55

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is W a subset of N?

A)Yes
B)No

Question 56

Evaluate the absolute value expression.

- $| 4 |$

A)0
B)-4
C)4
D)8

Question 57

Solve the problem.

-List the elements of S that are irrational numbers.

A) $\{ \sqrt { 3 } , \sqrt { 12 } \}$
B) $\left\{ - 5.27 , - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$
C) $\left\{ - 5.27 , - 5,0 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , \sqrt { 3 } , 3 , \sqrt { 12 } \right\}$
D) $\left\{ - 5.27 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } \right\}$

Question 58

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is W a subset of Q?

A)Yes
B)No

Question 59

Let R = the set of real numbers, N = the set of natural numbers, W = the set of whole numbers, I = the set of integers,
Q = the set of rational numbers, and H = the set of irrational numbers. Answer the question.
Is N a subset of W?

A)Yes
B)No

Question 60

Solve the problem.

-List the elements of S that are natural numbers.

A){0, 3}
B){3}
C) $\left\{ - 5.27 , - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$
D){-5, 0, 3}

Question 61

Evaluate the absolute value expression.

- $- | 16 |$

A)32
B)0
C)-16
D)16

Question 62

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $| - 21 |$ _________ $- 21$

A) $<$
B)=
C) $>$

Question 63

Evaluate the absolute value expression.

- $- | - 8.7 |$

A)0
B)-8.7
C)17.4
D)8.7

Question 64

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $- | - 4 |$ _________ $|-10|$

A) $<$
B)=
C) $>$

Question 65

List the values from smallest to largest.

- $- 7 , - 15 , - | 9 | , - | 22 | , - | - 17 |$

A) $- | 22 | , - | 9 | , - | - 17 | , - 15 , - 7$
B) $- | 22 | , - | - 17 | , - | 9 | , - 15 , - 7$
C) $- | 22 | , - 15 , - | - 17 | , - | 9 | , - 7$
D) $- | 22 | , - | - 17 | , - 15 , - | 9 | , - 7$

Question 66

Evaluate the absolute value expression.

- $| 0 |$

A)-1
B)1
C)0
D)undefined

Question 67

List the values from smallest to largest.

- $- 2.4 , - | - 2.1 | , - 2.3 , | - 2.4 | , - | - 2.7 | , - | 2.9 |$

A) $- | 2.9 | , - | - 2.7 | , - 2.3 , - 2.4 , - | - 2.1 | , | - 2.4 |$
B) $- | 2.9 | , - | - 2.7 | , - 2.4 , - 2.3 , - | - 2.1 | , | - 2.4 |$
C) $- | 2.9 | , - 2.4 , - | - 2.7 | , - 2.3 , - | - 2.1 | , | - 2.4 |$
D) $- | 2.9 | , - | - 2.7 | , - 2.4 , - | - 2.1 | , - 2.3 , | - 2.4 |$

Question 68

Evaluate the absolute value expression.

- $- | - 12 |$

A)0
B)-12
C)24
D)12

Question 69

Evaluate the absolute value expression.

- $- \left| - \frac { 6 } { 17 } \right|$

A)0
B) $\frac { 12 } { 17 }$
C) $- \frac { 6 } { 17 }$
D) $\frac { 6 } { 17 }$

Question 70

List the values from smallest to largest.

- $\left| - \frac { 2 } { 5 } \right| , - \left| \frac { 1 } { 2 } \right| , - \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 1 } { 2 } \right| , - \frac { 7 } { 8 }$

A) $- \frac { 7 } { 8 } , - \left| - \frac { 2 } { 5 } \right| , - \left| \frac { 1 } { 2 } \right| , \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 1 } { 2 } \right|$
B) $- \frac { 7 } { 8 } , - \left| \frac { 1 } { 2 } \right| , - \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 1 } { 2 } \right| , \left| - \frac { 2 } { 5 } \right|$
C) $- \frac { 7 } { 8 } , - \left| \frac { 1 } { 2 } \right| , - \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 1 } { 2 } \right|$
D) $- \left| \frac { 1 } { 2 } \right| , - \frac { 7 } { 8 } , - \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 2 } { 5 } \right| , \left| - \frac { 1 } { 2 } \right|$

Question 71

Evaluate.
3 + (-14)

A)-17
B)11
C)-11
D)17

Question 72

List the values from smallest to largest.

- $\pi , - \pi , | - 5 | , - | - 5 | , | - 2 | , - | - 2 |$

A) $- | - 5 | , - | - 2 | , - \pi , | - 2 | , \pi , | - 5 |$
B) $- | - 5 | , - \pi , - | - 2 | , \pi , | - 2 | , | - 5 |$
C) $- | - 5 | , - \pi , - | - 2 | , | - 2 | , | - 5 | , \pi$
D) $- | - 5 | , - \pi , - | - 2 | , | - 2 | , \pi , | - 5 |$

Question 73

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $| - 17 |$ _______ $- | 17 |$

A) $>$
B)=
C) $<$

Question 74

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $| - 7 |$ _______ $- 1$

A) $<$
B)=
C) $>$

Question 75

List the values from smallest to largest.

- $- 4 , | - 1 | , | 5 | , - | - 8 |$

A) $- 4 , - | - 8 | , | - 1 | , | 5 |$
B) $- | - 8 | , - 4 , | 5 | , | - 1 |$
C) $- | - 8 | , - 4 , | - 1 | , | 5 |$
D) $- | - 8 | , | - 1 | , - 4 , | 5 |$

Question 76

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $| - 8 |$ _______ $- | - 5 |$

A) $<$
B) $>$
C)=

Question 77

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $- 9 \_\_\_ | - 2 |$

A)=
B) $<$
C) $>$

Question 78

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

-| $| - 21 |$ _________ $| 21 |$

A)=
B) $>$
C) $<$

Question 79

Evaluate the absolute value expression.

- $- \left| \frac { 5 } { 7 } \right|$

A) $- \frac { 5 } { 7 }$
B) $\frac { 10 } { 7 }$
C) $\frac { 5 } { 7 }$
D)0

Question 80

$$\mathbf { Insert < , > , or = in~ the ~blank~ to~ make ~the ~statement~ true. }$$

- $| - 10 |$ ________ $| - 4 |$

A)=
B) $>$
C) $<$