Deck 2: Introduction to Logic and Sets

Question 1

Determine whether the following is a statement. If it is, then also classify the statement as true or false.

Answer 1

C

Question 2

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
Write the negation of the following: The test is difficult.

A)The test is not easy.
B)The test is very difficult.
C)The test is not difficult.
D)The test is not very easy.

Answer 2

C

Question 3

Construct a truth table for the statement.

Answer 3

A

Question 4

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
Can you bring the book?

A)False statement
B)True statement
C)Not a statement

Question 5

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
x + x = 6 (make true)

Question 6

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
Brazil is in Asia.

A)True statement
B)Not a statement
C)False statement

Question 7

Construct a truth table for the statement.

Question 8

Use a quantifier to make the following true or false, as indicated, where x is a natural number.

Question 9

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
x3 = 8 (make true)

Question 10

Use a quantifier to make the following true or false, as indicated, where x is a natural number.

Question 11

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
Negate the following: The store is sometimes open on Sunday.

Question 12

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
7x + y = 3

A)False statement
B)Not a statement
C)True statement

Question 13

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
x + y = x - y, where y = 0

A)Not a statement
B)True statement
C)False statement

Question 14

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
This room is big.

A)False statement
B)True statement
C)Not a statement

Question 15

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
2.4 = 5.2

A)Not a statement
B)False statement
C)True statement

Question 16

Use a quantifier to make the following true or false, as indicated, where x is a natural number.

Question 17

Use a quantifier to make the following true or false, as indicated, where x is a natural number.

Question 18

Construct a truth table for the statement.

Question 19

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
The state of California is in North America.

A)Not a statement
B)True statement
C)False statement

Question 20

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
5 - 1 = 4

A)True statement
B)Not a statement
C)False statement

Question 21

Restate in a logically equivalent form.
The flowers are not blooming or it is not winter.

A)It is not true that the flowers are blooming and it is winter.
B)The flowers are blooming and it is winter.
C)It is not true that both the flowers are blooming and it is winter.
D)It is not true that it is winter and the flowers are not blooming.

Question 22

Construct a truth table for the statement.

Question 23

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If I eat too much, then I'll exercise.

Question 24

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
I'll exercise if I don't eat too much.

Question 25

Construct a truth table for the statement.

Question 26

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If I exercise, then I won't eat too much.

Question 27

Construct a truth table for the statement.

Question 28

Restate in a logically equivalent form.
It is not true that both this book is interesting and the book is about stars.

A)This book cannot be both interesting and about stars.
B)Either this book is not interesting or it is not about stars.
C)This book is both interesting and about stars.
D)Either this book is interesting or it is about stars.

Question 29

Restate in a logically equivalent form.
It is not true that today I both went to school and read a book.

A)Today, I did not read a book and did not go to school.
B)Today, I read a book but did not go to school.
C)Today, I either did not go to school or I did not read a book.
D)Today, I went to school and read a book.

Question 30

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If I exercise, then the food won't be good and I won't eat too much.

Question 31

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If the food is not good, I won't eat too much.

Question 32

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If the food is good or if I eat too much, I'll exercise.

Question 33

Construct a truth table for the statement.

Question 34

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
If the food is good and if I eat too much, then I'll exercise.

Question 35

Construct a truth table for the statement.

Question 36

Restate in a logically equivalent form.

Question 37

Construct a truth table for the statement.

Question 38

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
I'll exercise if I eat too much.

Question 39

Restate in a logically equivalent form.
If it is clean, then it was washed.

A)If it is clean, then it was not washed.
B)If it is not clean, then it was not washed.
C)If it is clean, then it was washed.
D)If it was not washed, then it is not clean.

Question 40

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in
symbolic form.
The food is good and if I eat too much, then I'll exercise.

Question 41

Determine whether the statements are logically equivalent.

Question 42

State the converse of the following: If you study hard, then your grades will be good.

A)If you do not study hard, then your grades will not be good.
B)If you study hard, then your grades will not be good.
C)If your grades are good, then you studied hard.
D)If your grades are not good, then you did not study hard.

Question 43

Determine whether the statements are logically equivalent.

Question 44

Determine the validity of the argument.
Not all that glitters is gold. My ring glitters.
Therefore my ring is not gold.

A)Not valid
B)Valid

Question 45

State the converse of the following: If the four sides of a rectangle are equal, then it is a square.

A)If it is a square, then the four sides of a rectangle are equal.
B)If the four sides of a rectangle are equal, then it is not a square.
C)If it is not a square then the four sides of the rectangle are not equal.
D)If the four sides of a rectangle are not equal, then it is not a square.

Question 46

Determine whether the statements are logically equivalent.

Question 47

State the inverse of the following: If it is snowy, then it is cold.

A)If it is snowy, then it is not cold.
B)If it is cold, then it is snowy.
C)If it is not snowy, then it is not cold.
D)If it is not cold, then it is not snowy.

Question 48

Translate into symbolic form the following statement and explain: If it is not warm and
sunny, then we cannot go to the beach.

Question 49

Determine whether the statements are logically equivalent.

Question 50

State the inverse of the following: If you practice, then you will win.

A)If you practice, then you will not win.
B)If you do not win, then you did not practice.
C)If you win, then you practiced.
D)If you do not practice, then you will not win.

Question 51

State the contrapositive of the following: If he is happy, then he is smiling.

A)If he is smiling, then he is happy.
B)If he is happy, then he is not smiling.
C)If he is not happy, then he is not smiling.
D)If he is not smiling, then he is not happy.

Question 52

Determine whether the statements are logically equivalent.

Question 53

State the contrapositive of the following: If it is pouring, then it is raining.

A)If it is not pouring, then it is not raining.
B)If it is pouring, then it is not raining.
C)If it is raining, then it is pouring.
D)If it is not raining, then it is not pouring.

Question 54

Determine whether the statements are logically equivalent.

Question 55

Determine whether the statements are logically equivalent.

Question 56

Determine whether the statements are logically equivalent.

Question 57

Restate in a logically equivalent form.
It is not tasty or it is not sour.

A)If it is sour, then it is tasty.
B)It is not true that it is both tasty and sour.
C)If it is not tasty, then it is not sour.
D)If it is tasty, then it is sour.

Question 58

Determine whether the statements are logically equivalent.

Question 59

Determine whether the statements are logically equivalent.

Question 60

Restate in a logically equivalent form.
If a triangle is equilateral, then its sides are equal.

A)If the sides of a triangle are equal, then it is not equilateral.
B)If a triangle is not equilateral, then its sides are equal.
C)If the sides of a triangle are not equal, then it is equilateral.
D)If the sides of a triangle are not equal, then it is not equilateral.

Question 61

Determine the validity of the argument.
Some investments are risky. Real estate is an investment.
Therefore real estate is risky.

A)Not valid
B)Valid

Question 62

Determine the validity of the argument.
Not all cars are considered sporty. Not all cars are safe at high speeds.
Therefore sports cars are safe at high speeds.

A)Not valid
B)Valid

Question 63

Determine the validity of the argument.
All businessmen wear suits. Aaron wears suits.
Therefore Aaron is a businessman.

A)Not valid
B)Valid

Question 64

Write a valid conclusion based on the statements.
Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

A)Careful drivers are happy.
B)People who smile are alert.
C)Careful drivers have accidents.
D)People who smile have accidents.

Question 65

Determine the validity of the argument.
Some winter days are cold. Today, it is cold.
Therefore it is winter.

A)Not valid
B)Valid

Question 66

Write a valid conclusion based on the statements.
Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold.

A)Hard workers don't get colds.
B)Hard workers don't go to work.
C)Anyone who sweats works hard.
D)Anyone who has a cold works hard.

Question 67

Determine the validity of the argument.
Martians are green. Roger is not green.
Therefore Roger is not a Martian.

A)Valid
B)Not valid

Question 68

Write a valid conclusion based on the statements.
It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

A)The squirrels are scurrying.
B)Squirrels do not scurry during the day.
C)The squirrels are not scurrying.
D)Squirrels do not scurry at night.

Question 69

Determine the validity of the argument.
Martians are green. Frogs are green.
Therefore frogs are Martians.

A)Valid
B)Not valid

Question 70

Determine the validity of the argument.
Sailboats need a windy day to sail. Today is a windy day.
Therefore today is a good day for sailing sailboats.

A)Valid
B)Not valid

Question 71

Write a valid conclusion based on the statements.
Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television.

A)Students who watch TV will be barred from watching TV.
B)Students who watch TV while doing homework will not be allowed to watch TV.
C)Students who watch TV will be grounded.
D)Students who are grounded watch TV while doing homework.

Question 72

Determine the validity of the argument.
Some TV shows are comedies. All comedies are hits.
Therefore some TV shows are hits.

A)Valid
B)Not valid

Question 73

Write a valid conclusion based on the statements.
If it's not Saturday, then Dad will shave. If Dad has whiskers, then he did not shave. If it's Saturday, then Dad will take us to the game.

A)If Dad has whiskers, then he will take us to the game.
B)If Dad takes us to the game, then he has whiskers.
C)If Dad shaves, then it's not Saturday.
D)If Dad did not shave, then he has whiskers.

Question 74

Write a valid conclusion based on the statements.
All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

A)Any dead animal has no heartbeat.
B)All fish have a heartbeat.
C)Any dead fish can dream.
D)All live animals can dream.

Question 75

Write a valid conclusion based on the statements.
If I get robbed, I will go to court. I got robbed.

A)I will go to court.
B)I will not go to court.
C)I will not get robbed in court.
D)I will get robbed in court.

Question 76

Determine the validity of the argument.
Football and studying don't mix. Don is a football player.
Therefore Don does not study.

A)Valid
B)Not valid

Question 77

Write a valid conclusion based on the statements.
If you pay your taxes, then you are a good citizen. People who do not pay their taxes did not receive a tax bill. If it is April, then you will receive a tax bill. It is April.

A)You did not receive a tax bill.
B)You did not pay your taxes.
C)You are a good citizen.
D)You are not a good citizen.

Question 78

Determine the validity of the following conclusion and explain: If you walk fast, then you
will reach the bus stop on time. If you reach the bus stop on time, then you will catch the
bus. If you walk fast, then you will catch the bus.

Question 79

Write a valid conclusion based on the statements.
All birds have wings. None of my pets are birds. All animals with wings can flap them.

A)No birds can flap their wings.
B)All my pets can flap their wings.
C)All birds can flap their wings.
D)None of my pets can flap their wings.

Question 80

Write a valid conclusion based on the statements.
Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

A)Every man with a mind can apply himself.
B)Every distracted man can apply himself.
C)Every man with a mind is distracted.
D)Every man who can apply himself has a mind.