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If every member of one set $B$ is also a member of a second set $A$, then $B$ is called a __________ of $A$.

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If $A$ and $B$ are two sets, the set that contains all members that are in sets $A$ and $B$ or both is called the __________ of $A$ and $B$.

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If $A$ and $B$ are two sets, the set that contains all members that are in both sets is called the __________ of $A$ and $B$.

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A real number is any number that can be expressed as a __________ .

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A __________ is a letter that is used to represent a number.

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All integers that are exactly divisible by 2 are called __________ integers.

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Natural numbers greater than 1 that are not prime are called __________ numbers.

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Fractions such as $\frac{2}{3}, \frac{8}{2},$ and $-\frac{7}{9}$ are called __________ numbers.

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Irrational numbers are __________ that don't terminate and don't repeat.

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The symbol __________ is read as "is less than or equal to."

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The only integer that is neither positive nor negative is __________.

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The Associative Property of Addition states that $(x+y)+z=$ __________.

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The Commutative Property of Multiplication states that $x y=$ __________.

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Use the Distributive Property to complete the statement: $5(m+2)=$ __________.

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The statement $(m+n) p=p(m+n)$ illustrates the _____________ Property of __________.

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The graph of an __________ is a portion of a number line.

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The graph of an open interval has _________ endpoints.

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The graph of a closed interval has __________ endpoints.

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Except for $0,$ the absolute value of every number is __________.

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The __________ between two distinct points on a number line is always positive.

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$\mathrm{N} \subset \mathrm{W}$$

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$Q \subset R$$

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$\mathrm{Q} \subset \mathrm{N}$$

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$\mathrm{Z} \subset \mathrm{Q}$$

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$\mathrm{W} \subset \mathrm{Z}$$

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Let

$\mathbf{N}=$the set of natural numbers

$\mathbf{W}=$the set of whole numbers

$\mathbf{Z}=$the set of integers

$\mathbf{Q}=$the set of rational numbers

$\mathbf{R}=$the set of real numbers

Determine whether each statement is true or false. Read the symbol $c$ as "is a subset of."

$$\mathbf{R} \subset \mathbf{Z}$$

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Let $A=\{a, b, c, d, e\}, B=(d, e, f, g\},$ and $C=\{a, c, e, f\} .$ Find each set.

$$A \cup B$$

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Let $A=\{a, b, c, d, e\}, B=(d, e, f, g\},$ and $C=\{a, c, e, f\} .$ Find each set.

$$A \cap B$$

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Let $A=\{a, b, c, d, e\}, B=(d, e, f, g\},$ and $C=\{a, c, e, f\} .$ Find each set.

$$A \cap C$$

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Let $A=\{a, b, c, d, e\}, B=(d, e, f, g\},$ and $C=\{a, c, e, f\} .$ Find each set.

$$B \cup C$$

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Determine whether the decimal form of each fraction terminates or repeats.

$$\frac{9}{16}$$

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Determine whether the decimal form of each fraction terminates or repeats.

$$\frac{3}{8}$$

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Determine whether the decimal form of each fraction terminates or repeats.

$$\frac{3}{11}$$

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Determine whether the decimal form of each fraction terminates or repeats.

$$\frac{5}{12}$$

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are natural numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are whole numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are integers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are rational numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are irrational numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are prime numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are composite numbers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are even integers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are odd integers?

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Consider the following set:

$$\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$$

Which numbers are negative numbers?

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Graph each subset of the real numbers on a number line.

The natural numbers between 1 and 5

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Graph each subset of the real numbers on a number line.

The composite numbers less than 10

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Graph each subset of the real numbers on a number line.

The prime numbers between 10 and 20

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Graph each subset of the real numbers on a number line.

The integers from $-2$ to $4$

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Graph each subset of the real numbers on a number line.

The integers between $-5$ and $0$

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Graph each subset of the real numbers on a number line.

The even integers between $-9$ and $-1$

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Graph each subset of the real numbers on a number line.

The odd integers between $-6$ and $4$

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Graph each subset of the real numbers on a number line.

$-0.7,1.75,$ and $3 \frac{7}{8}$

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Write each inequality in interval notation and graph the interval.

$$x>2$$

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Write each inequality in interval notation and graph the interval.

$$x<4$$

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Write each inequality in interval notation and graph the interval.

$$0<x<5$$

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Write each inequality in interval notation and graph the interval.

$$-2<x<3$$

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Write each inequality in interval notation and graph the interval.

$$x>-4$$

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Write each inequality in interval notation and graph the interval.

$$x<3$$

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Write each inequality in interval notation and graph the interval.

$$-2 \leq x<2$$

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Write each inequality in interval notation and graph the interval.

$$-4<x \leq 1$$

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Write each inequality in interval notation and graph the interval.

$$x \leq 5$$

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Write each inequality in interval notation and graph the interval.

$$x \geq-1$$

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Write each inequality in interval notation and graph the interval.

$$-5<x \leq 0$$

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Write each inequality in interval notation and graph the interval.

$$-3 \leq x<4$$

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Write each inequality in interval notation and graph the interval.

$$-2 \leq x \leq 3$$

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Write each inequality in interval notation and graph the interval.

$$-4 \leq x \leq 4$$

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Write each inequality in interval notation and graph the interval.

$$6 \geq x \geq 2$$

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Write each inequality in interval notation and graph the interval.

$$3 \geq x \geq-2$$

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Write each pair of inequalities as the intersection of two intervals and graph the result.

$$x>-5 \text { and } x<4$$

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Write each pair of inequalities as the intersection of two intervals and graph the result.

$$x \geq-3 \text { and } x<6$$

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Write each pair of inequalities as the intersection of two intervals and graph the result.

$$x \geq-8 \text { and } x \leq-3$$

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Write each pair of inequalities as the intersection of two intervals and graph the result.

$$x>1 \text { and } x \leq 7$$

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Write each inequality as the union of two intervals and graph the result.

$$x<-2 \text { or } x>2$$

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Write each inequality as the union of two intervals and graph the result.

$$x \leq-5 \text { or } x>0$$

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Write each inequality as the union of two intervals and graph the result.

$$x \leq-1 \text { or } x \geq 3$$

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Write each inequality as the union of two intervals and graph the result.

$$x<-3 \text { or } x \geq 2$$

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Write each expression without using absolute value symbols.

$$|\pi-\pi|$$

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Write each expression without using absolute value symbols.

$$|x+1| \text { and } x \geq 2$$

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Write each expression without using absolute value symbols.

$$|x+1| \text { and } x \leq-2$$

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Write each expression without using absolute value symbols.

$$|x-4| \text { and } x<0$$

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Write each expression without using absolute value symbols.

$$|x-7| \text { and } x>10$$

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Find the distance between each pair of points on the number line.

3 and 8

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Find the distance between each pair of points on the number line.

-5 and 12

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Find the distance between each pair of points on the number line.

-8 and -3

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Find the distance between each pair of points on the number line.

6 and -20

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What subset of the real numbers would you use to describe the populations of Memphis and Miami?

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What subset of the real numbers would you use to describe the subdivisions of an inch on a ruler?

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Find the distance between each pair of points on the number line.

What subset of the real numbers would you use to report temperatures in London and Lisbon?

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What subset of the real numbers would you use to describe the prices of hoodies at Aéropostale?

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The average low temperature in International Falls, Minnesota, in January is $-7^{\circ} \mathrm{F}$. The average high temperature is $15^{\circ} \mathrm{F}$. Determine the degrees difference between the average high and the average low.

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Harbin, China, is one of the world's coldest cities and known for its ice and snow festivals. In February, the average nightly low temperature is $-20^{\circ} \mathrm{C}$ and the average daily high temperature is $-7^{\circ} \mathrm{C}$. What is the temperature drop from day to night?

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Is the statement $\left|\frac{a}{b}\right|=\frac{|a|}{|b|}(b \neq 0)$ always true? Explain.

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

There are six integers between $-3$ and $3$.

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

$\frac{725}{0}$ is a rational number because $725$ and $0$ are integers.

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

$\infty$ is a real number.

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

$$|a-b|=|b-a|$$

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

$$\varnothing \subset\left\{5, \pi, \sqrt{3}, \frac{13}{4}\right\}$$

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

$$\varnothing \subset \varnothing$$

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

There are six subsets of $\{11,22,33\}$.

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Determine if the statement is true or false. If the statement is false, then correct it and make it true.

A set is always a subset of itself.

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