Section 1
Sets of Real Numbers
Fill in the blanks.A _________ is a collection of objects.
Fill in the blanks.If every member of one set $B$ is also a member of a _______ second set $A,$ then $B$ is called a _______ of $A$.
Fill in the blanks.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.
Fill in the blanks.If $A$ and $B$ are two sets, the set that contains all members that are in both sets is called the ______ of $A$ and $B$
Fill in the blanks.A real number is any number that can be expressed as a _______.
Fill in the blanks.A _______ is a letter that is used to represent a number.
Fill in the blanks.The smallest prime number is ________.
Fill in the blanks.All integers that are exactly divisible by 2 are called ______ integers.
Fill in the blanks.Natural numbers greater than I that are not prime are called ______ numbers.
Fill in the blanks.Fractions such as $\frac{2}{3}, \frac{8}{2},$ and $-\frac{7}{9}$ are called ______ numbers.
Fill in the blanks.Irrational numbers are ______ that don't terminate and don't repeat.
Fill in the blanks.The symbol ______ is read as "is less than or equal to."
Fill in the blanks.On a number line, the ______ numbers are to the left of $0 .$
Fill in the blanks.The only integer that is neither positive nor negative is ______.
Fill in the blanks.The Associative Property of Addition states that (x+y)+z= ______.
Fill in the blanks.The Commutative Property of Multiplication states that $x y=$ ______.
Fill in the blanks.Use the Distributive Property to complete the statement: $5(m+2)=$ ______.
Fill in the blanks.The statement $(m+n) p=p(m+n)$ illustrates the ______ Property of ______.
Fill in the blanks.The graph of an ______ is a portion of a number line.
Fill in the blanks.The graph of an open interval has ______ endpoints.
Fill in the blanks.The graph of a closed interval has ______ endpoints.
Fill in the blanks.The graph of a ______ interval has one endpoint.
Fill in the blanks.Except for $0,$ the absolute value of every number is ______.
Fill in the blanks.The ______ between two distinct points on a number line is always positive.
Let$\mathbf{N}=$ the set of natural mumbers$\mathbf{W}=$ the set of whole numbers$\boldsymbol{Z}=$ the set of integers $\mathbf{Q}=$ the set of rational mumbers$\mathbf{R}=$ the set of real mumbersDetermine whether each statement is true or false. Read the symbol $\subset$ as "is a subset of."
$\mathrm{N} \subset \mathrm{W}$
$Q \subset R$
$\mathrm{Q} \subset \mathrm{N}$
$\mathbf{Z} \subset \mathbf{Q}$
$\mathrm{W} \subset \mathrm{Z}$
$\mathbf{R} \subset \mathbf{Z}$
Let $A=\{\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{e}\}, B=(\mathbf{d}, \mathbf{e}, \mathbf{f}, \mathbf{g}\},$ and $C=\{\mathbf{a}, \mathbf{c}, \mathbf{e}, \mathbf{f}\} .$ Find each set.$A \cup B$
Let $A=\{\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{e}\}, B=(\mathbf{d}, \mathbf{e}, \mathbf{f}, \mathbf{g}\},$ and $C=\{\mathbf{a}, \mathbf{c}, \mathbf{e}, \mathbf{f}\} .$ Find each set.$A \cap B$
Let $A=\{\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{e}\}, B=(\mathbf{d}, \mathbf{e}, \mathbf{f}, \mathbf{g}\},$ and $C=\{\mathbf{a}, \mathbf{c}, \mathbf{e}, \mathbf{f}\} .$ Find each set.$A \cap C$
Let $A=\{\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{e}\}, B=(\mathbf{d}, \mathbf{e}, \mathbf{f}, \mathbf{g}\},$ and $C=\{\mathbf{a}, \mathbf{c}, \mathbf{e}, \mathbf{f}\} .$ Find each set.$B \cup C$
Determine whether the decimal form of each fraction terminates or repeats.$$\frac{9}{16}$$
Determine whether the decimal form of each fraction terminates or repeats.$$\frac{3}{8}$$
Determine whether the decimal form of each fraction terminates or repeats.$$\frac{3}{11}$$
Determine whether the decimal form of each fraction terminates or repeats.$$\frac{5}{12}$$
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?
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?
Consider the following set: $\left\{-5,-4,-\frac{2}{3}, 0,1, \sqrt{2}, 2,2.75,6,7\right\}$Which numbers are integers?
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?
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?
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?
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?
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?
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?
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?
Graph each subset of the real numbers on a number line.The natural numbers between 1 and 5
Graph each subset of the real numbers on a number line.The composite numbers less than 10
Graph each subset of the real numbers on a number line.The prime numbers between 10 and 20
Graph each subset of the real numbers on a number line.The integers from $-2$ to 4
Graph each subset of the real numbers on a number line.The integers between $-5$ and 0
Graph each subset of the real numbers on a number line.The even integers between $-9$ and $-1$
Graph each subset of the real numbers on a number line.The odd integers between $-6$ and 4
Graph each subset of the real numbers on a number line.$$-0.7,1.75, \text { and } 3 \frac{7}{8}$$
Write each inequality in interval notation and graph the interval.$$x>2$$
Write each inequality in interval notation and graph the interval.$$x<4$$
Write each inequality in interval notation and graph the interval.$$0<x<5$$
Write each inequality in interval notation and graph the interval.$$-2<x<3$$
Write each inequality in interval notation and graph the interval.$$x>-4$$
Write each inequality in interval notation and graph the interval.$$x<3$$
Write each inequality in interval notation and graph the interval.$$-2 \leq x<2$$
Write each inequality in interval notation and graph the interval.$$-4<x \leq 1$$
Write each inequality in interval notation and graph the interval.$$x \leq 5$$
Write each inequality in interval notation and graph the interval.$$x \geq-1$$
Write each inequality in interval notation and graph the interval.$$-5<x \leq 0$$
Write each inequality in interval notation and graph the interval.$$-3 \leq x<4$$
Write each inequality in interval notation and graph the interval.$$-2 \leq x \leq 3$$
Write each inequality in interval notation and graph the interval.$$-4 \leq x \leq 4$$
Write each inequality in interval notation and graph the interval.$$6 \geq x \geq 2$$
Write each inequality in interval notation and graph the interval.$$3 \geq x \geqq-2$$
Write each pair of inequalities as the intersection of two intervals and graph the result.$$x>-5 \text { and } x<4$$
Write each pair of inequalities as the intersection of two intervals and graph the result.$$x \geq-3 \text { and } x<6$$
Write each pair of inequalities as the intersection of two intervals and graph the result.$$x \geq-8 \text { and } x \leq-3$$
Write each pair of inequalities as the intersection of two intervals and graph the result.$$x>1 \text { and } x \leq 7$$
Write each inequality as the union of two intervals and graph the result.$$x<-2 \text { or } x>2$$
Write each inequality as the union of two intervals and graph the result.$$x \leq-5 \text { or } x>0$$
Write each inequality as the union of two intervals and graph the result.$$x \leq-1 \text { or } x \geq 3$$
Write each inequality as the union of two intervals and graph the result.$$x<-3 \text { or } x \geq 2$$
Write each expression without using absolute value symbols.$$|13|$$
Write each expression without using absolute value symbols.$$|-17|$$
Write each expression without using absolute value symbols.$$|0|$$
Write each expression without using absolute value symbols.$$-|63|$$
Write each expression without using absolute value symbols.$$-|-8|$$
Write each expression without using absolute value symbols.$$|-25|$$
Write each expression without using absolute value symbols.$$-|32|$$
Write each expression without using absolute value symbols.$$-|-6|$$
Write each expression without using absolute value symbols.$$|\pi-5|$$
Write each expression without using absolute value symbols.$$|8-\pi|$$
Write each expression without using absolute value symbols.$$\pi-\pi$$
Write each expression without using absolute value symbols.$$|2 \pi|$$
Write each expression without using absolute value symbols.$$x+1 | \text { and } x \geq 2$$
Write each expression without using absolute value symbols.$$|x+1| \text { and } x \leq-2$$
Write each expression without using absolute value symbols.$$|x-4| \text { and } x<0$$
Write each expression without using absolute value symbols.$$|x-7| \text { and } x>10$$
Find the distance between each pair of points on the number line.3 and 8
Find the distance between each pair of points on the number line. -5 and 12
Find the distance between each pair of points on the number line.$-8$ and $-3$
Find the distance between each pair of points on the number line.6 and $-20$
What subset of the real numbers would you use to describe the populations of several cities?
What subset of the real numbers would you use to describe the subdivisions of an inch on a ruler?
What subset of the real numbers would you use to report temperatures in several cities?
What subset of the real numbers would you use to describe the financial condition of a business?
Explain why $-x$ could be positive.
Explain why every integer is a rational number.
Is the statement $|a b|=|a| \cdot|b|$ always true? Explain.
Is the statement $\left|\frac{a}{b}\right|=\frac{|a|}{|b|}(b \neq 0)$ always true? Explain.
Is the statement $|a+b|=|a|+|b|$ always true? Explain.
Under what conditions will the statement given in Exercise 109 be true?
Explain why it is incorrect to write $a<b>c$ if $a<b$ and $b>c$
Explain why $|b-a|=|a-b|$