Deck 3: Logic

Question 1

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Answer 1

B

Question 2

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Jim does not play football and Michael does not play basketball.

Answer 2

D

Question 3

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Answer 3

B

Question 4

Write a negation of the statement.
All dinosaurs were carnivores.

A) All dinosaurs were not carnivores.
B) Some dinosaurs were not carnivores.
C) No dinosaurs were carnivores.
D) Some dinosaurs were carnivores.

Question 5

Write a negation of the statement.
Everyone is asleep.

A) Everyone is not asleep.
B) None are asleep.
C) Everyone is awake.
D) Not everyone is asleep.

Question 6

Write a negation of the statement.
Some citizens obey traffic laws.

A) All citizens obey traffic laws.
B) No citizens do not obey traffic laws.
C) Some citizens do not obey traffic laws.
D) No citizens obey traffic laws.

Question 7

Write a negation of the statement.
No fifth graders play soccer.

A) Some fifth graders play soccer.
B) Everybody plays soccer.
C) Fifth graders play soccer.
D) Everybody does not play soccer.

Question 8

Write a negation of the statement.
She earns more than me.

A) She earns the same as me.
B) She earns less than me.
C) She does not earn more than me.
D) She does not earn less than me.

Question 9

Write a negation of the statement.
All squares are parallelograms.

A) Some squares are parallelograms.
B) Some squares are not parallelograms.
C) All squares are not parallelograms.
D) No squares are parallelograms.

Question 10

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Question 11

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Neither Jim plays football nor Michael plays basketball.

Question 12

Write a negation of the statement.
Some athletes are musicians.

A) All athletes are musicians.
B) All athletes are not musicians.
C) Some athletes are not musicians.
D) No athletes are musicians.

Question 13

Write a negation of the statement.
Some photographs are not displayed at this exhibition.

A) No photographs are displayed at this exhibition.
B) Some photographs are displayed at this exhibition.
C) All photographs are displayed at this exhibition.
D) All photographs are not displayed at this exhibition.

Question 14

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Question 15

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Question 16

Write a negation of the statement.
Not all people like football.

A) Some people do not like football.
B) Some people like football.
C) All people like football.
D) All people do not like football.

Question 17

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Question 18

Write a negation of the statement.
Some people donʹt like walking.

A) Some people like walking.
B) All people like walking.
C) Nobody likes walking.
D) Some people donʹt like driving.

Question 19

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.

Question 20

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
The car is in the garage and the bicycle is in the driveway.

Question 21

Convert the compound statement into words.

A) It is not the case that students are happy and teachers are not happy.
B) It is not the case that students are happy or teachers are not happy.
C) Students are not happy or teachers are not happy.
D) Students are not happy and teachers are not happy.

Question 22

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Jim plays football and Michael plays basketball. )p

Question 23

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If the food is good, then I eat too much. p

Question 24

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Jim does not play football and Michael plays basketball.

Question 25

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If the food is not good, I wonʹt eat too much.

Question 26

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If I eat too much, then Iʹll exercise. p

Question 27

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If the food is good and if I eat too much, then Iʹll exercise.

Question 28

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
Iʹll exercise if I donʹt eat too much.

Question 29

Convert the compound statement into words.

A) It is not the case that fossil fuels pollute the air and people buy large houses.
B) Fossil fuels pollute the air and people buy large houses.
C) People buy large houses and fossil fuels do not pollute the air.
D) Fossil fuels pollute the air or people buy large houses.

Question 30

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
It is not the case that Jim does not play football and Michael does not play basketball.

Question 31

Convert the compound statement into words.

Question 32

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Jim does not play football or Michael plays basketball.

Question 33

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
Jim does not play football or Michael does not play basketball.

Question 34

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
Iʹll exercise if I eat too much.

Question 35

Convert the compound statement into words.

A) We eat a lot and the food tastes delicious or nobody has dessert.
B) We do not eat a lot or the food tastes delicious and nobody has dessert.
C) We eat a lot or the food tastes delicious or nobody has dessert.
D) We eat a lot or the food tastes delicious and nobody has dessert.

Question 36

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If I exercise, then I wonʹt eat too much.

Question 37

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
The food is good and if I eat too much, then Iʹll exercise.

A) (r ∧ p) → qB)r ∧ (p → q)
C) (r ∨ p) → qD)(r → p) ∨ q

Question 38

Convert the compound statement into words.

A) Babies wear plastic bibs and babies eat bananas.
B) Babies eat bananas or babies do not wear plastic bibs.
C) Babies eat bananas and babies wear plastic bibs.
D) Babies eat bananas or babies wear plastic bibs.

Question 39

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If the food is good or if I eat too much, Iʹll exercise.

Question 40

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
If I exercise, then the food wonʹt be good and I wonʹt eat too much.

Question 41

Write the compound statement in words.

A) The puppy is trained if the puppy behaves well and his owners are happy.
B) If the puppy is trained then the puppy behaves well, and his owners are happy.
C) The puppy is trained, and if the puppy behaves well then his owners are happy.
D) The puppy is trained, or if the puppy behaves well then his owners are happy.

Question 42

Construct a truth table for the statement.

Question 43

Convert the compound statement into words.

A) We do not eat a lot and the food tastes delicious and nobody has dessert.
B) We eat a lot or the food tastes delicious and nobody has dessert.
C) We do not eat a lot or the food tastes delicious or nobody has dessert.
D) We do not eat a lot or the food tastes delicious and nobody has dessert.

Question 44

Answer the question.
If tomorrow is not Saturday then today is Friday if and only if tomorrow is Saturday.

Question 45

Construct a truth table for the statement.

Question 46

Answer the question.
It is not true that if you take your vitamins you will stay healthy.

Question 47

Write the compound statement in words.

A) The puppy behaves well and his owners are happy.
B) It is not the case that if the puppy behaves well then his owners are happy.
C) The puppy behaves well or his owners are happy.
D) If the puppy does not behave well then his owners are not happy.

Question 48

Answer the question.
A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of:
Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes,
And pasta. Is this order permissible?

A) No
B) Yes

Question 49

Construct a truth table for the statement.

Question 50

Write the compound statement in words.

A) The puppy is not trained or the puppy does not behave well, and his owners are not happy.
B) If the puppy is not trained or the puppy does not behave well, then his owners are not happy.
C) If the puppy is not trained then the puppy does not behave well and his owners are not happy.
D) If the puppy is not trained and the puppy does not behave well, then his owners are not happy.

Question 51

Write the compound statement in words.

A) The puppy behaves well or the puppy is trained.
B) If the puppy is trained then the puppy behaves well.
C) The puppy does not behave well or the puppy is not trained.
D) If the puppy behaves well then the puppy is trained.

Question 52

Write the compound statement in words.

A) If the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional.
B) It is not true that if the monitor is included or the color printer is optional, then the zip drive is extra and the color printer is not optional.
C) It is not true that if the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional.
D) If the monitor is included and the color printer is optional, then it is not true that the zip drive is extra or the color printer is not optional.

Question 53

Write the compound statement in words.

A) If the puppy is not trained then his owners are not happy.
B) The puppy is not trained and his owners are not happy.
C) It is not the case that if the puppy is trained then his owners are happy.
D) The puppy is trained or his owners are happy.

Question 54

Answer the question.
If people drive small cars then people will use less fuel and the ozone hole will not expand.

Question 55

Write the compound statement in words.

A) If the color printer is optional, then the monitor is not included and the zip drive is extra.
B) The color printer is not optional if and only if the monitor is not included and the zip drive is extra.
C) If the color printer is not optional, then the monitor is not included and the zip drive is extra.
D) The color printer is optional if and only if the monitor is not included and the zip drive is extra.

Question 56

Answer the question.
If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible
By 6.

Question 57

Answer the question.
Pat Rabbit did not go into Mr. McNoodleʹs garden and Molly collected blueberries.

Question 58

Write the compound statement in words.

A) If the puppy is trained, then the puppy behaves well and his owners are happy.
B) If the puppy is trained and the puppy behaves well, then his owners are happy.
C) The puppy is trained and the puppy behaves well if his owners are happy.
D) The puppy is trained, the puppy behaves well, and his owners are happy.

Question 59

Write the compound statement in words.

A) If the puppy is trained, then the puppy behaves will and his owners are happy.
B) The puppy is trained and the puppy behaves well if his owners are happy.
C) If the puppy is trained or the puppy behaves well, then his owners are happy.
D) If the puppy is trained and the puppy behaves well, then his owners are happy.

Question 60

Answer the question.
The lights are on if and only if it is not midnight or it is wintertime.

Question 61

Construct a truth table for the statement.

- $(r \wedge p) \wedge(\sim p \vee t)$

A)
$\begin{array} { c c c c } \mathrm { r } & \mathrm { p } & \mathrm { t } & ( \mathrm { r } \wedge \mathrm { p } ) \wedge ( \sim \mathrm { p } \vee \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { c c c c } \mathrm { r } & \mathrm { p } & \mathrm { t } & ( \mathrm { r } \wedge \mathrm { p } ) \wedge ( \sim \mathrm { p } \vee \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 62

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 63

Construct a truth table for the statement.

- $(p \wedge t) \vee(\sim p \wedge \sim t)$

A)
$\begin{array} { l l c } \mathrm { p } & \mathrm { t } & ( \mathrm { p } \wedge \mathrm { t } ) \vee ( \sim \mathrm { p } \wedge \sim \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { c c c } \mathrm { p } & \mathrm { t } & ( \mathrm { p } \wedge \mathrm { t } ) \vee ( \sim \mathrm { p } \wedge \sim \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
C)
$\begin{array} { l l c } \mathrm { p } & \mathrm { t } & ( \mathrm { p } \wedge \mathrm { t } ) \vee ( \sim \mathrm { p } \wedge \sim \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c } \mathrm { p } & \mathrm { t } & ( \mathrm { p } \wedge \mathrm { t } ) \vee ( \sim \mathrm { p } \wedge \sim \mathrm { t } ) \\\hline \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F }\end{array}$

Question 64

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ The garden contains sunflowers.
$\mathrm{q}=$ The fence is painted white.
$\mathrm{r}=$ The lawnmower is electric.
The garden contains sunflowers or the fence is painted white, or the lawnmower is electric.

A)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \mathrm { q } ) \vee \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
B)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \mathrm { q } ) \vee \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \mathrm { q } ) \vee \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \mathrm { q } ) \vee \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 65

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 66

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ Parker will work in an office.
$\mathrm{q}$ = Parker will work as a forest ranger.
$\mathrm{r}=$ Parker will work as a landscape architect.
Parker will not work in an office, but he will work as a forest ranger or a landscape architect.

A)
$\begin{array} { l l l c } \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { l l l c } \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
D)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & \sim \mathrm { p } \wedge ( \mathrm { q } \vee \mathrm { r } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 67

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 68

Construct a truth table for the statement.

- $\sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s})$

A)
$\begin{array} { l l c } \mathrm { s } & \mathrm { t } & \sim \left( \mathrm { s } _ { \vee } \mathrm { t } \right) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { l l c } \mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c c } \mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { l l c } \mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 69

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 70

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 71

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ The forest is dark.
$\mathrm{q}=$ The moon is full.
The forest is dark or the moon is full.

A)
$\begin{array} { l l l } \mathrm { p } & \mathrm { q } & \mathrm { p } \vee \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
B)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \mathrm { p } \vee \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c r } \mathrm { p } & \mathrm { q } & \mathrm { p } \wedge \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \mathrm { p } \vee \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$

Question 72

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ At most, 100 guests arrived at the wedding reception.
$\mathrm{q}=$ There was a lot of cake left over.
It is not the case that, at most, 100 guests arrived at the wedding reception and there was a lot of cake left over.

A)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
B)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
C)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
D)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 73

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 74

Construct a truth table for the statement.

Question 75

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 76

Construct a truth table for the statement.

-
$W \vee(W \wedge \sim W)$

A)
$$\begin{array} { c c } \mathrm { W } & \mathrm { W } \vee ( \mathrm { W } \wedge \sim \mathrm { W } ) \\\hline \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F }\end{array}$$
B)
$$\begin{array} { c c } \mathrm { W } & \mathrm { W } \vee ( \mathrm { W } \wedge \sim \mathrm { W } ) \\\hline \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T }\end{array}$$
C)
$$\begin{array} { c c } \mathrm { W } & \mathrm { W } \vee ( \mathrm { W } \wedge \sim \mathrm { W } ) \\\hline \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { T }\end{array}$$
D)
$$\begin{array} { c c } \mathrm { W } & \mathrm { W } \vee ( \mathrm { w } \wedge \sim \mathrm { W } ) \\\hline \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F }\end{array}$$

Question 77

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ The doctor prescribed medicine.
$\mathrm{q}=$ The patient has recovered.
The doctor did not prescribe medicine but the patient recovered.

A)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { c c r } \mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c } \mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 78

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.

Question 79

Construct a truth table for the statement.

- $\sim(\sim(s \vee p))$

A)
$\begin{array} { c c c } \mathrm { s } & \mathrm { p } & \sim ( \sim ( \mathrm { s } \vee \mathrm { p } ) ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
B)
$\begin{array} { c c c } \mathrm { s } & \mathrm { p } & \sim ( \sim ( \mathrm { s } \vee \mathrm { p } ) ) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
C)
$\begin{array} { c c c } \mathrm { s } & \mathrm { p } & \sim ( \sim ( \mathrm { s } \vee \mathrm { p } ) ) \\\hline \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c } \mathrm { s } & \mathrm { p } & \sim \left( \sim \left( \mathrm { s } _ { \vee } \mathrm { p } \right) \right) \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$

Question 80

Translate the statement into symbols then construct a truth table.

- $\mathrm{p}=$ The cab is late.
$\mathrm{q}$ = The plane takes off on time.
$\mathrm{r}=$ Nancy has her plane ticket.
The cab is late or the plane does not take off on time, and Nancy does not have her ticke

A)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \sim \mathrm { q } ) \wedge \sim \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$
B)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \sim \mathrm { q } ) \wedge \sim \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
C)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \sim \mathrm { q } ) \wedge \sim \mathrm { r } \\\mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }\end{array}$
D)
$\begin{array} { c c c c } \mathrm { p } & \mathrm { q } & \mathrm { r } & ( \mathrm { p } \vee \sim \mathrm { q } ) \wedge \sim \mathrm { r } \\\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \\\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \\\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }\end{array}$