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Section 1
What Is Algebra? Introduction and Basic Notation
Indicate whether the given statement is true or false.$$3 \in\{1,3,5,8\}$$
Indicate whether the given statement is true or false.$$5 \in(1,3,5,8)$$
Indicate whether the given statement is true or false.$$8 \notin\{2,3,5,7,9\}$$
Indicate whether the given statement is true or false.$$7 \in\{2,4,6,9,17\}$$
Indicate whether the given statement is true or false.$$\mathbf{a} \in\{\mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{a}\}$$
Indicate whether the given statement is true or false.$$\mathbf{g} \notin\{\mathbf{r}, \mathbf{g}, \mathbf{c}, \mathbf{b}\}$$
Indicate whether the given statement is true or false.$$17 \in N$$
Indicate whether the given statement is true or false.$$12 \notin N$$
Indicate whether the given statement is true or false.$$0 \in N$$
Indicate whether the given statement is true or false.$$0 \in W$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{x | x \text { is a natural number less than } 8\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{x | x \in N \text { and } x<8\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{y | y \text { is an even number less than } 20\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{m | m \text { is an odd number greater than } 7\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{x | x \leq 6\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{n | n<9\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{x | x<6\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{n | n \geq 9\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{x | x \geq 6\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{n | n>9\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{x | x>6\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$$\{n | n \leq 9\}$$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{a | a \text { is greater than } 2 \text { and less than } 6\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{a | a \text { is greater than } 6 \text { and less than } 2\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{t | t \text { is a factor of } 24\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{t | t \text { is a factor of } 30\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{f | f \text { is a factor of } 12 \text { or a factor of } 15\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{f | f \text { is a factor of } 12 \text { and a factor of } 15\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{m | m \text { is a multiple of } 4\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{n | n \text { is a multiple of } 5\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{m | m \text { is a multiple of } 3 \text { and a multiple of } 4\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{n | n \text { is a multiple of } 2 \text { and a multiple of } 5\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{x | x \text { is a multiple of } 10 \text { and not divisible by } 5\}$
List the elements of each of the given sets. Unless otherwise specified, assume that all numbers are whole numbers.$\{y | y \text { is a multiple of } 5 \text { and not divisible by } 10\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$A=\{x | x \text { is an odd natural number less than } 20\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$B=\{x | x \text { is an even natural number less than } 20\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$C=\{t | t \text { is a natural number less than } 50 \text { that ends in a } 5\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$D=\{w | w \text { is a natural number less than } 60 \text { that ends in a } 0\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$S=\{t | t \text { is a natural number greater than } 20 \text { that ends in a double zero }\}$
Find another description of the set using set-builder notation and also list the set using the roster method.$T=\{w | w \text { is a natural number greater than } 40 \text { that ends in a triple zero }\}$
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 4_____2.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 8_____20.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 7_____7.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 5_____0.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 19_____24 - 10.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 18 - 5____10 + 4.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 19 + 53_____72.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 16_____12 + 4.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 8 - 8_____4 $\cdot$ 0.
Fill in the appropriate ordering symbol: either $<,>,$ or $=$. 8 + 0____4 $\cdot$0.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.5____8.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.17____12.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.43_____43.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.5____2+4.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.$4 \cdot 2$_____4 + 2.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.$1 \cdot 2$_____1 + 2.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.$6 \cdot 0$_____6 + 0.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.25 - 5____14 + 3.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.16____12 - 5.
In Exercises $51-60,$ fill in as many of the following ordering symbols as make the statement true.Choose from $<, \leq,>, \geq,=, \neq$.4 - 4_____$17 \cdot 0$.
Factor the given number into its prime factors. If the number is prime, say so.$$14$$
Factor the given number into its prime factors. If the number is prime, say so.$$26$$
Factor the given number into its prime factors. If the number is prime, say so.$$33$$
Factor the given number into its prime factors. If the number is prime, say so.$$35$$
Factor the given number into its prime factors. If the number is prime, say so.$$30$$
Factor the given number into its prime factors. If the number is prime, say so.$$50$$
Factor the given number into its prime factors. If the number is prime, say so.$$37$$
Factor the given number into its prime factors. If the number is prime, say so.$$80$$
Factor the given number into its prime factors. If the number is prime, say so.$$64$$
Factor the given number into its prime factors. If the number is prime, say so.$$41$$
Factor the given number into its prime factors. If the number is prime, say so.$$96$$
Factor the given number into its prime factors. If the number is prime, say so.$$120$$
Factor the given number into its prime factors. If the number is prime, say so.$$87$$
Factor the given number into its prime factors. If the number is prime, say so.$$91$$
Factor the given number into its prime factors. If the number is prime, say so.$$360$$
Factor the given number into its prime factors. If the number is prime, say so.$$420$$
Factor the given number into its prime factors. If the number is prime, say so.$$126$$
Factor the given number into its prime factors. If the number is prime, say so.$$165$$
Factor the given number into its prime factors. If the number is prime, say so.$$858$$
Factor the given number into its prime factors. If the number is prime, say so.$$561$$
Factor the given number into its prime factors. If the number is prime, say so.$$912$$
Factor the given number into its prime factors. If the number is prime, say so.$$1,332$$
Factor the given number into its prime factors. If the number is prime, say so.$$1,904$$
Factor the given number into its prime factors. If the number is prime, say so.$$3,024$$
Graph the given set on a number line.$$\{0,3,7\}$$
Graph the given set on a number line.$\{x | x \text { is an even natural number less than } 10\}$
Graph the given set on a number line.$\{a | a \text { is a natural number less than } 12 \text { and not divisible by } 3\}$
Graph the given set on a number line.$$\{1,4,5,8\}$$
What is the difference between the set $N$ (the set of natural numbers) and the set $W$ (the set of whole numbers)?
What is the difference between a term and a factor? Give an example to illustrate the difference.
What is the difference between a factor and a multiple? Give an example to illustrate the difference.
Let set $A$ be the first ten multiples of 2 and let set $B$ be the first ten multiples of3. Let $C$ be the set of numbers both sets have in common. How would you describe set $C$ ?
Repeat Exercise 92 with multiples of 4 and $6 .$ Is the description of set $C$ similar? Why or why not?
Describe each of the following expressions as a sum or a product. If the expression is a sum, list the terms. If the expression is a product, list the factors.(a) $x+y+z$(b) $x y z$(c) $x y+z$(d) $x(y+z)$