# Finite Mathematics and Calculus with Applications

## Educators

Problem 1

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
Montevideo is the capital of Uruguay.

Check back soon!

Problem 2

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
John Jay was the first chief justice of the United States.

Check back soon!

Problem 3

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
Don't feed the animals.

Check back soon!

Problem 4

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
Do unto others as you would have them do unto you.

Check back soon!

Problem 5

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
$2+2=5$ and $3+3=7$

Check back soon!

Problem 6

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
$x < 7$ or $x > 14$

Check back soon!

Problem 7

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
Got milk?

Check back soon!

Problem 8

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
Is that all there is?

Check back soon!

Problem 9

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
I am not a crook.

Check back soon!

Problem 10

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
China does not have a population of more than 1 billion.

Check back soon!

Problem 11

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
She enjoyed the comedy team of Penn and Teller.

Check back soon!

Problem 12

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
The New Hampshire motto is "Live free or die."

Check back soon!

Problem 13

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
If I get an A.I will celebrate.

Check back soon!

Problem 14

Decide whether each of the following is a statement. If it is a statement, decide whether or not it is compound.
If it's past $8 : 00,$ then we are late.

Check back soon!

Problem 15

Write a negation for each statement.
My favorite flavor is chocolate.

Check back soon!

Problem 16

Write a negation for each statement.
This is not the time to complain.

Check back soon!

Problem 17

Give a negation of each inequality.
$$y>12$$

Check back soon!

Problem 18

Give a negation of each inequality.
$$x<-6$$

Check back soon!

Problem 19

Give a negation of each inequality.
$$q \geq 5$$

Check back soon!

Problem 20

Give a negation of each inequality.
$$r \leq 19$$

Check back soon!

Problem 21

Try to negate the sentence "The exact number of words in this sentence is $10^{\prime \prime}$ and see what happens. Explain the problem that arises.

Check back soon!

Problem 22

Explain why the negation of $" r>4 "$ is not $^{4} r<4 . "$

Check back soon!

Problem 23

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$\sim b$

Check back soon!

Problem 24

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$-d$

Check back soon!

Problem 25

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$\sim b \vee d$

Check back soon!

Problem 26

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$b \wedge \sim d$

Check back soon!

Problem 27

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$\sim(b \wedge \sim d)$

Check back soon!

Problem 28

Let $b$ represent the statement "I'm getting better" and $d$ represent the statement "My parrot is dead." Translate each symbolic statement into words.
$\sim(b \vee d)$

Check back soon!

Problem 29

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $q$ is false, what must be the truth value of $(p \wedge \sim q) \wedge q ?$

Check back soon!

Problem 30

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $q$ is true, what must be the truth value of $q \vee(q \wedge \sim p) ?$

Check back soon!

Problem 31

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $p \wedge q$ is true, then $q$ must be

Check back soon!

Problem 32

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $p \vee q$ is false, and $p$ is false, then $q$ must be _______

Check back soon!

Problem 33

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $\sim(p \vee q)$ is true, what must be the truth values of each of the component statements?

Check back soon!

Problem 34

Use the concepts introduced in this section to answer Exercises $29-34 .$
If $-(p \wedge q)$ is false, what must be the truth values of the component statements?

Check back soon!

Problem 35

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim p$

Check back soon!

Problem 36

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim q$

Check back soon!

Problem 37

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$p \vee q$

Check back soon!

Problem 38

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$. p \wedge q$

Check back soon!

Problem 39

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$p \vee \sim q$

Check back soon!

Problem 40

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim p \wedge q$

Check back soon!

Problem 41

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim p \vee \sim q$

Check back soon!

Problem 42

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$p \wedge \sim q$

Check back soon!

Problem 43

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim(p \wedge \sim q)$

Check back soon!

Problem 44

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim(\sim p \vee \sim q)$

Check back soon!

Problem 45

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim[\sim p \wedge(\sim q \vee p)]$

Check back soon!

Problem 46

Let $p$ represent a false statement and let $q$ represent a true statement. Find the truth value of each compound statement.
$\sim[(\sim p \wedge \sim q) \vee \sim q]$

Check back soon!

Problem 47

Is the statement $3 \geqq 1$ a conjunction or a disjunction? Why?

Check back soon!

Problem 48

Why is the statement $6 \geq 2$ true? Why is $6 \geq 6$ true?

Check back soon!

Problem 49

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$(p \wedge r) \vee \sim q$$

Check back soon!

Problem 50

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$(q \vee \sim r) \wedge p$$

Check back soon!

Problem 51

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$p \wedge(q \vee r)$$

Check back soon!

Problem 52

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$(\sim p \wedge q) \vee \sim r$$

Check back soon!

Problem 53

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$\sim(p \wedge q) \wedge(r \vee \sim q)$$

Check back soon!

Problem 54

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$(\sim p \wedge \sim q) \vee(\sim r \wedge q)$$

Check back soon!

Problem 55

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$\sim[(\sim p \wedge q) \vee r]$$

Check back soon!

Problem 56

Let $p$ represent a true statement, and $q$ and $r$ represent false statements. Find the truth value of each compound statement.
$$\sim[r \vee(\sim q \wedge \sim p)]$$

Check back soon!

Problem 57

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$p \wedge r$$

Check back soon!

Problem 58

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$p \vee \sim q$$

Check back soon!

Problem 59

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$\sim q \vee \sim r$$

Check back soon!

Problem 60

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$\sim p \wedge \sim r$$

Check back soon!

Problem 61

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$(p \wedge q) \vee r$$

Check back soon!

Problem 62

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$\sim p \vee(\sim r \vee \sim q)$$

Check back soon!

Problem 63

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$(\sim r \wedge q) \vee \sim p$$

Check back soon!

Problem 64

Let $p$ represent the statement $" 2 > 7,$ " let $q$ represent the statement $" 8 \leq 6, "$ and let $r$ represent the statement $^{6} 19 \leq 19^{39}$ Find the truth value of each compound statement.
$$\sim(p \vee \sim q) \vee \sim r$$

Check back soon!

Problem 65

Income Tax The following excerpts appear in a guide for preparing income tax reports. Source: Your Income Tax 2010 .
Which of these excerpts are statements?

Check back soon!

Problem 66

Income Tax The following excerpts appear in a guide for preparing income tax reports. Source: Your Income Tax 2010 .
Which of these excerpts are compound statements?

Check back soon!

Problem 67

Income Tax The following excerpts appear in a guide for preparing income tax reports. Source: Your Income Tax 2010 .
Write the negation of excerpt d.

Check back soon!

Problem 68

Income Tax The following excerpts appear in a guide for preparing income tax reports. Source: Your Income Tax 2010 .
Determine $p$ and $q$ to symbolically represent excerpt c.

Check back soon!

Problem 69

Technology For Exercises $69-74$ , let $a$ represent the statement "Apple Computer, Inc. developed the iPad," and $j$ represent the statement, "Steve Jobs is the CEO of Apple Computer, Inc." Convert each compound statement into symbols.
Apple Computer, Inc. developed the iPad, and Steve Jobs is the CEO of Apple Computer, Inc.

Check back soon!

Problem 70

Technology For Exercises $69-74$ , let $a$ represent the statement "Apple Computer, Inc. developed the iPad," and $j$ represent the statement, "Steve Jobs is the CEO of Apple Computer, Inc." Convert each compound statement into symbols.
Apple Computer, Inc. did not develop the iPad, and Steve Jobs is not the CEO of Apple Computer, Inc.

Check back soon!

Problem 71

Technology For Exercises $69-74$ , let $a$ represent the statement "Apple Computer, Inc. developed the iPad," and $j$ represent the statement, "Steve Jobs is the CEO of Apple Computer, Inc." Convert each compound statement into symbols.

Apple Computer, Inc, did not develop the iPad, or Steve Jobs is the CEO of Apple Computer, Inc.

Check back soon!

Problem 72

Technology For Exercises $69-74$ , let $a$ represent the statement "Apple Computer, Inc. developed the iPad," and $j$ represent the statement, "Steve Jobs is the CEO of Apple Computer, Inc." Convert each compound statement into symbols.

Apple Computer, Inc. developed the iPad, or Steve Jobs is the CEO of Apple Computer, Inc.

Check back soon!

Problem 73

Technology For Exercises $69-74$ , let $a$ represent the statement "Apple Computer, Inc. developed the iPad," and $j$ represent the statement, "Steve Jobs is the CEO of Apple Computer, Inc." Convert each compound statement into symbols.

Suppose the statements that Apple Computer, Inc. developed the iPad and that Steve Jobs is CEO of Apple Computer, Inc. are both true. Which of Exercises $69-72$ are true statements?

Check back soon!

Problem 74

Suppose the statements that Apple Computer, Inc. developed the iPad and that Steve Jobs is CEO of Apple Computer, Inc. are both false. Which of Exercises $69-72$ are true statements?

Check back soon!

Problem 75

Medicine The following excerpts appear in a home medical reference book. Source: American College of Physicians Complete Home Medical Guide.
Which of these excerpts are statements?

Check back soon!

Problem 76

Medicine The following excerpts appear in a home medical reference book. Source: American College of Physicians Complete Home Medical Guide.
Which of these excerpts are compound statements?

Check back soon!

Problem 77

Medicine The following excerpts appear in a home medical reference book. Source: American College of Physicians Complete Home Medical Guide.
Write the negation of excerpt e.

Check back soon!

Problem 78

Law The following excerpts appear in a guide to common laws. Source: Law for Dummies.
Which of these excerpts are statements?

Check back soon!

Problem 79

Law The following excerpts appear in a guide to common laws. Source: Law for Dummies.
Which of these excepts are compound statements?

Check back soon!

Problem 80

Law The following excerpts appear in a guide to common laws. Source: Law for Dummies.
Write the negation of excerpt e.

Check back soon!

Problem 81

Philosophy Read each of the following quotes from ancient philosophers. Provide an argument why these quotes may or may not be called statements. Source: Masterworks of Philosophy.
a. "A friend is a friend of someone."-Socrates
b. "Every art, and every science reduced to a teachable form, and in like manner every action and moral choice, aims, it is thought, at some good: for which reason a common and by no means a bad description of what the Chief Good is, 'that which all things aim at." "- Aristotle
c. “Furthermore, Friendship helps the young to keep from error: the old, in respect of attention and such deficiencies in action as their weakness makes them liable to; and those who are in their prime, in respect of noble deeds, because they are thus more able to devise plans and carry them out.”—Aristotle

Check back soon!

Problem 82

Bible Read each of the following quotes from the biblical book Proverbs. Provide an argument why these quotes may or may not be called statements. Source: TNIV Bible.
a. "A gentle answer turns away wrath." -Proverbs $15 : 1$
b. "The hot-tempered stir up dissension, but those who are patient calm a quarrel." Proverbs $15 : 18$
c. "When justice is done, it brings joy to the righteous but terror to evildoers," - Proverbs $21 : 15$
d. "Do not exploit the poor because they are poor and do not crush the needy in court."- Proverbs $22 : 22$
e. "Apply your heart to instruction and your ears to words of knowledge."- Proverbs $23 : 12$

Check back soon!

Problem 83

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

New Orleans won the Super Bowl but Peyton Manning is not the best quarterback.

Check back soon!

Problem 84

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

New Orleans did not win the Super Bowl or Peyton Manning is not the best quarterback.

Check back soon!

Problem 85

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

New Orleans did not win the Super Bowl or Peyton Manning is not the best ouarterback.

Check back soon!

Problem 86

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

New Orleans did not win the Super Bowl but Peyton Manning is the best quarterback.

Check back soon!

Problem 87

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

Neither did New Orleans win the Super Bowl nor is Peyton Manning the best quarterback.

Check back soon!

Problem 88

Football For Exercises $83-88,$ let $n$ represent the statement "New Orleans won the Super Bowl" and $m$ represent the statement "Peyton Manning is the best quarterback." Convert each compound statement into symbols.

Either New Orleans won the Super Bowl or Peyton Manning is the best quarterback, and it is not the case that both New Orleans won the Super Bowl and Peyton Manning is the best quarterback.

Check back soon!

Problem 89

APPLY IT Suppose the statements that New Orleans won the Super Bowl and that Peyton Manning is the best quarterback are both true. Which of Exercises $83-88$ are true statements?

Check back soon!

Problem 90

Suppose the statements that New Orleans won the Super Bowl and that Peyton Manning is the best quarterback are both false. Which of Exercises $83-88$ are true statements?

Check back soon!