Question 1

Evaluate the absolute value expression.
-$| - 4 |$
A)-4
B)0
C)8
D)4

Accepted Answer

The absolute value of a number is its distance from 0 on the number line, regardless of direction. Therefore, $| - 4 | = 4$.

Question 2

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}

Accepted Answer

The answer of Solve the problem.
-List the elements of S...

Question 3

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

Accepted Answer

A rational number is any number that can be expressed as a ratio of two integers. An irrational number is any number that cannot be expressed as a ratio of two integers. Therefore, Q and I are disjoint sets, and Q is not a subset of I. No, because rational numbers (Q) can be expressed as a ratio of two integers, while irrational numbers (I) cannot be expressed as a ratio of two integers. Therefore, there are no elements that belong to both sets.

Question 4

Evaluate the absolute value expression.
-$\left| - \frac { 17 } { 22 } \right|$
A)0
B) $\frac { 17 } { 22 }$
C) $\frac { 17 } { 11 }$
D) $- \frac { 17 } { 22 }$

Accepted Answer

The absolute value of a number is its distance from 0 on the number line, regardless of direction. Therefore, $\left| - \frac { 17 } { 22 } \right|$ equals $\frac { 17 } { 22 }$, making choice B correct.

Question 5

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

Accepted Answer

Every integer is a rational number (it can be expressed as a fraction where the denominator is 1), so the set of integers is a subset of the set of rational numbers.

Question 6

Evaluate the absolute value expression.
-$\left|\frac { 4 } { 11 }\right|$
A) $\frac { 4 } { 11 }$
B) $- \frac { 4 } { 11 }$
C)0
D) $\frac { 8 } { 11 }$

Accepted Answer

The absolute value of a number is its distance from 0 on the number line, which is always non-negative. Therefore, $\left|\frac { 4 } { 11 }\right| = \frac { 4 } { 11 }$.

Question 7

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

Accepted Answer

The elements of S that are real numbers are: -5.27, -5, 0, 1/3, 4/7, 107/121, √3, 3, and √12.

Question 8

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

Accepted Answer

Yes, Q is a subset of R because every rational number can be expressed as a ratio of two integers and therefore can be represented as a decimal that either terminates or repeats. All terminating and repeating decimals are also real numbers, so Q is a subset of R. Every rational number can be expressed as a quotient of two integers, so every rational number is also a real number. Therefore, Q is a subset of R.

Question 9

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}

Accepted Answer

The answer of Solve the problem.
-From the Venn diagram, determine...

Question 10

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) $\left\{ - 5 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } , 3 \right\}$

Accepted Answer

The answer of Solve the problem.
-List the elements of S...

Question 11

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}

Accepted Answer

The answer of Solve the problem.
-List the elements of S...

Question 12

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

Accepted Answer

All irrational numbers are real numbers, but not all real numbers are irrational. Therefore, H is a subset of R. By definition, the set of irrational numbers (H) consists of all real numbers that are not rational, which means they cannot be expressed as a ratio of two integers. Since all real numbers are contained in R, H is a subset of R.

Question 13

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

Accepted Answer

The set of rational numbers (Q) and the set of irrational numbers (H) are disjoint sets, meaning they have no elements in common. Therefore, Q cannot be a subset of H, and the answer is option B. The definition of rational numbers is any number that can be expressed as a fraction of two integers. The definition of irrational numbers is any number that cannot be expressed as a fraction of two integers. Therefore, there is no overlap between the two sets and Q cannot be a subset of H.

Question 14

Evaluate the absolute value expression.
-| $| - 23.5 |$
A)47
B)23.5
C)-23.5
D)0

Accepted Answer

The absolute value of any number is always non-negative, and the absolute value of -23.5 is 23.5.

Question 15

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

Accepted Answer

The answer of Let R = the set of real...

Question 16

Evaluate the absolute value expression.
-$| 4 |$
A)0
B)-4
C)4
D)8

Accepted Answer

The absolute value of a number is its distance from 0 on the number line, without considering direction. The absolute value of 4 is 4.

Question 17

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) $\left\{ - 5.27 , \frac { 1 } { 3 } , \frac { 4 } { 7 } , \frac { 107 } { 121 } \right\}$

Accepted Answer

The answer of Solve the problem.
-List the elements of S...

Question 18

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

Accepted Answer

Every whole number is a rational number, since it can be expressed as a/b, where a and b are both integers and b is not equal to 0. Therefore, W is a subset of Q. Every whole number is a rational number because it can be written as a fraction with a denominator of 1. Therefore, W is a subset of Q.

Question 19

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

Accepted Answer

Every natural number is a whole number, so N is a subset of W. N is a subset of W because every natural number is also a whole number.

Question 20

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}

Accepted Answer

Natural numbers are positive integers starting from 1. Among the given options, only {3} fits this definition as it contains a positive integer without any negative numbers or fractions.

Quiz 1: Basic Concepts

Evaluate the absolute value expression. - $| - 4 |$

Solve the problem. -List the elements of S that are integers.

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?

Evaluate the absolute value expression. - $\left| - \frac { 17 } { 22 } \right|$

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?

Evaluate the absolute value expression. - $\left|\frac { 4 } { 11 }\right|$

Solve the problem. -List the elements of S that are real numbers.

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?

Solve the problem. -From the Venn diagram, determine the set A.

Solve the problem. -List the elements of S that are rational numbers.

Solve the problem. -List the elements of S that are whole numbers.

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?

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?

Evaluate the absolute value expression. -| $| - 23.5 |$

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?

Evaluate the absolute value expression. - $| 4 |$

Solve the problem. -List the elements of S that are irrational numbers.

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?

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?

Solve the problem. -List the elements of S that are natural numbers.

Quiz 1: Basic Concepts

Evaluate the absolute value expression. - ∣−4∣| - 4 |∣−4∣

Solve the problem. -List the elements of S that are integers.

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?

Evaluate the absolute value expression. - ∣−1722∣\left| - \frac { 17 } { 22 } \right|​−2217​​

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?

Evaluate the absolute value expression. - ∣411∣\left|\frac { 4 } { 11 }\right|​114​​

Solve the problem. -List the elements of S that are real numbers.

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?

Solve the problem. -From the Venn diagram, determine the set A.

Solve the problem. -List the elements of S that are rational numbers.

Solve the problem. -List the elements of S that are whole numbers.

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?

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?

Evaluate the absolute value expression. -| ∣−23.5∣| - 23.5 |∣−23.5∣

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?

Evaluate the absolute value expression. - ∣4∣| 4 |∣4∣

Solve the problem. -List the elements of S that are irrational numbers.

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?

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?

Solve the problem. -List the elements of S that are natural numbers.

Evaluate the absolute value expression. - $| - 4 |$

Evaluate the absolute value expression. - $\left| - \frac { 17 } { 22 } \right|$

Evaluate the absolute value expression. - $\left|\frac { 4 } { 11 }\right|$

Evaluate the absolute value expression. -| $| - 23.5 |$

Evaluate the absolute value expression. - $| 4 |$