Deck 3: Logic

Question 1

Answer 1

Question 2

Answer 2

Question 3

Which of the following is a simple statement?

A) February is the shortest month.
B) If you don't use sunblock, you'll get burned.
C) His eyes are neither blue nor brown.
D) He has a dog and a cat.

Answer 3

A

Question 4

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words.

Question 5

Question 6

Which sentence is not a statement?

A) It's raining.
B) Jan and Ella are neighbors.
C) Who is your instructor?
D) 5 × 5 = 10

Question 7

Question 8

Let p = "My homework is finished." Write the following statement in symbols. It is not true that my homework is finished.

Question 9

Let p = "Daphne speaks Spanish." Let q = "Daphne speaks French." Write the following statement in symbols. Daphne speaks Spanish if and only if Daphne speaks French.

Question 10

Let p = "Ed plays the guitar." Let q = "Ed plays the piano." Write the following statement in symbols. It is false that Ed does not play the guitar or Ed plays the piano.

Question 11

Decide if the statement is simple or compound. I will go with you if and only if we are on time.

Question 12

Question 13

Question 14

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. Paolo does not bicycle to school, or Roberto drives to school.

Question 15

Draw an Euler circle diagram for the statement. Some teachers are nice people.

Question 16

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. If Paolo does not bicycle to school, then Roberto does not drive to school.

Question 17

Question 18

Decide whether each statement is simple or compound.

Question 19

Question 20

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words.

Question 21

A new weight loss supplement claims that if you take this product daily and you cut your calorie intake by 10%, you will lose at least 10 pounds in the next 4 months. If you use the product daily and you don't cut your calorie intake by 10%, and then don't lose 10 pounds, is the claim made by the advertiser true or false?

Question 22

Question 23

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. It is not true that Paolo does not bicycle to school and Roberto does not drive to school.

Question 24

Determine if the two statements are logically equivalent, negations, or neither.
$$p \vee \sim q ; \sim p \wedge q$$

A) Neither
B) Logically equivalent
C) Negations

Question 25

Write the negation of the statement. She is not angry.

Question 26

Question 27

Is the following sentence a statement? Neither Ben nor Alonzo is going camping.

Question 28

Let p = "Ed plays the guitar." Let q = "Ed plays the piano." Write the following statement in symbols. Ed plays the guitar, and Ed does not play the piano.

Question 29

Determine whether the statement is a tautology, a self-contradiction, or neither.
$$( \sim p \rightarrow q ) \vee ( p \vee \sim q )$$

A) Self-contradiction
B) Tautology
C) Neither

Question 30

Identify the statement as a conjunction, disjunction, conditional, or biconditional. If Jon fails this test, then he will fail the course.

A) Biconditional
B) Disjunction
C) Conditional
D) Conjunction

Question 31

Question 32

Let p = "I am hungry." Let q = "I am going to have a snack." Write the following statement in words.

Question 33

Question 34

Draw an Euler circle diagram for the statement. No math classes are easy.

Question 35

Question 36

State whether the sentence is a statement or not. Close the door.

Question 37

Question 38

Question 39

Question 40

Determine whether the argument is valid or invalid. Some fizzbangers are breakdancers.
No breakdancers are jealous.
$\therefore$ Some fizzbangers are not jealous.

A) Invalid
B) Valid

Question 41

Determine the validity of the following argument.
$\begin{array} { l } q \rightarrow \sim p \\\frac { q } { \therefore \sim p }\end{array}$

A) Valid
B) Invalid

Question 42

Question 43

Write the negation of the statement. Everyone at my house got the flu.

A) Not everyone at my house got the flu.
B) No one at my house got the flu.
C) Someone at my house got the flu.

Question 44

Question 45

Determine whether the statement is a tautology, a self-contradiction, or neither.
$$( \sim p \vee q ) \wedge ( p \vee \sim q )$$

A) Self-contradiction
B) Tautology
C) Neither

Question 46

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies.
$\begin{array} { l } \sim p \vee q \\\sim q \\\hline \therefore \sim p\end{array}$

A) Valid
B) Invalid

Question 47

Identify the quantifier in the statement as either universal or existential. At least one of the children was blond.

A) Universal
B) Existential

Question 48

Write the converse of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

A) If my parents do not pay for my insurance, I get a speeding ticket.
B) If my parents pay for my insurance, I do not get a speeding ticket.
C) If I get a speeding ticket, my parents pay for my insurance.
D) If I do not get a speeding ticket, my parents pay for my insurance.

Question 49

Question 50

Determine whether the argument is valid or invalid.
Some children are energetic.
Some children are not polite.
$\therefore$ Some polite people are not energetic.

A) Invalid
B) Valid

Question 51

Determine whether the argument is valid or invalid.
Some $R$ is not $S$ .
No $S$ is $T$ .
$\therefore$ Some $R$ is not $T$ .

A) Valid
B) Invalid

Question 52

Determine whether the argument is valid or invalid.
All $B$ is $C$ .
All $C$ is $A$ .
$\therefore$ All $B$ is $A$ .

A) Invalid
B) Valid

Question 53

Determine the validity of the following argument.
$\begin{array} { c } \sim p \rightarrow q \\q \rightarrow \sim r \\\hline \therefore \sim p \rightarrow \sim r\end{array}$

A) Invalid
B) Valid

Question 54

Determine whether the argument is valid or invalid.
Some items are non-sale items.
No non-sale item is affordable.
$\therefore$ Some items are not affordable.

A) Invalid
B) Valid

Question 55

Construct a truth table for the following statement.
$\sim p \wedge q$
How many T's are in the final column?

A) 2
B) 3
C) 4
D) 1

Question 56

A new intelligence enhancing supplement claims that if you take this product daily and you get 8 hours of sleep per night, you will increase your score by 5 points on a standard IQ test. Let p be "you take this product daily," q be "you get 8 hours of sleep per night," and r be "you will increase your score by 5 points on a standard IQ test." Write the compound statement in symbolic form, using conjunctions and the conditional.

Question 57

Determine the validity of the following argument.
$\begin{array} { l } \sim p \vee q \\\frac { q \rightarrow \sim r } { \therefore \sim r }\end{array}$

A) Invalid
B) Valid

Question 58

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies.
$\begin{array} { c } \sim p \rightarrow q \\\sim r \rightarrow q \\\hline \therefore \sim p \rightarrow r\end{array}$

A) Valid
B) Invalid

Question 59

Identify the statement as a conjunction, disjunction, conditional, or biconditional. We will build a pool if and only if we win the lottery.

A) Conditional
B) Conjunction
C) Biconditional
D) Disjunction

Question 60

Identify the quantifier in the statement as universal or existential. Then write the negation of the statement. At least one breed of cat is hairless.

A) Existential, All breeds of cat are hairless.
B) Universal, All breeds of cat are hairless.
C) Universal, Some breeds of cat have hair.
D) Existential, No breed of cat is hairless.

Question 61

Determine if the two statements are logically equivalent, negations, or neither.
$$\sim p \rightarrow q ; \sim p \vee q$$

A) Negations
B) Logically equivalent
C) Neither

Question 62

Determine whether each sentence is a statement or not.
i. $2 \times 3 = 0$
ii. Please don't yell.
iii. She went to Spain.
iv. Kel studied for hours.

A) Yes, Yes, No, Yes
B) Yes, No, Yes, Yes
C) No, No, No, Yes
D) No, Yes, Yes, Yes

Question 63

Determine if the two statements are logically equivalent, negations, or neither.
$$( p \wedge q ) \rightarrow \sim r ; r \rightarrow ( \sim p \vee \sim q )$$

A) Neither
B) Negations
C) Logically equivalent

Question 64

Determine if the two statements are logically equivalent, negations, or neither.
$$p \rightarrow \sim q ; q \rightarrow \sim p$$

A) Negations
B) Neither
C) Logically equivalent

Question 65

Write the contrapositive of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

A) If my parents do not pay for my insurance, I get a speeding ticket.
B) If I get a speeding ticket, my parents pay for my insurance.
C) If I do not get a speeding ticket, my parents pay for my insurance.
D) If my parents pay for my insurance, I do not get a speeding ticket.

Question 66

Write the converse of the conditional statement. I will buy a new computer if my laptop breaks.

A) If my laptop doesn't break, then I won't buy a new computer.
B) If I don't buy a new computer, then my laptop will break.
C) If I buy a new computer then my laptop will break
D) If I don't buy a new computer, then my laptop won't break.

Question 67

Question 68

Write the inverse of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

A) If my parents do not pay for my insurance, I get a speeding ticket.
B) If I get a speeding ticket, my parents pay for my insurance.
C) If I do not get a speeding ticket, my parents pay for my insurance.
D) If my parents pay for my insurance, I do not get a speeding ticket.

Question 69

Use De Morgan's laws to write the negation of the statement. The towel is wet or it isn't striped.

A) The towel is not wet and it is striped.
B) The towel is not wet or it is striped.
C) The towel is not wet or it isn't striped.
D) The towel is not wet and it isn't striped.

Question 70

Determine whether the statement is a tautology, a self-contradiction, or neither.
$( p \leftrightarrow q ) \wedge ( p \leftrightarrow q )$

A) Tautology
B) Neither
C) Self-contradiction

Question 71

Question 72

Question 73

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies.
$$\begin{array} { l } \sim p \rightarrow q \\\sim q \\\hline \therefore p\end{array}$$

A) Valid
B) Invalid

Question 74

Determine if the two statements are logically equivalent, negations, or neither.
$$( p \vee q ) \wedge \sim r ; \sim ( p \wedge q ) \vee r$$

A) Neither
B) Logically equivalent
C) Negations

Question 75

Use De Morgan's laws to write the negation of the statement. The towel is wet and it isn't striped.

A) The towel is not wet or it is striped.
B) The towel is not wet or it isn't striped.
C) The towel is not wet and it isn't striped.
D) The towel is not wet and it is striped.

Question 76

Write the contrapositive of the conditional statement. I will buy a new computer if my laptop breaks.

A) If my laptop doesn't break, then I won't buy a new computer.
B) If I don't buy a new computer, then my laptop won't break.
C) If I don't buy a new computer, then my laptop will break.
D) If I buy a new computer then my laptop will break

Question 77

Classify each statement as simple or compound.
i. Jeff's brother is two years old.
ii. $\mathrm { He }$ is over six feet tall.
iii. His parents own two houses.
iv. He likes cats and dogs.

A) Simple, Simple, Simple, Compound
B) Compound, Simple, Compound, Simple
C) Simple, Compound, Simple, Compound
D) Compound, Simple, Simple, Simple

Question 78

Determine the validity of the following argument.
$\begin{array} { l } \sim q \rightarrow p \\q \\\hline \therefore \sim p \end{array}$

A) Invalid
B) Valid

Question 79

Write the negation of the statement. It is not true that my mother is from outer space

A) My mother is from outer space.
B) My mother is not from outer space.
C) It is true that my mother is not from outer space.

Question 80