Question 1

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

Accepted Answer

A)  Neither 
B)  Logically equivalent 
C)  Negations 
A)  Neither 
B)  Logically equivalent 
C)  Negations

Question 2

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.

Accepted Answer

The answer of Let p = "Ed plays the guitar."...

Question 3

Let p = "I am hungry." Let q = "I am going to have a snack." Write the following statement in words. $$\sim p \wedge ( q \rightarrow p )$$

Accepted Answer

I am not hungry; and

Question 4

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

Accepted Answer

A)  Universal 
B)  Existential 
A)  Universal 
B)  Existential

Question 5

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

Accepted Answer

A)  Invalid 
B)  Valid 
A)  Invalid 
B)  Valid

Question 6

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

Accepted Answer

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. 
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 7

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

Accepted Answer

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. 
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 8

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

Accepted Answer

Sally's mom is thirt

Question 9

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.

Accepted Answer

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. 
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 10

Write the argument in symbols; then decide whether the argument is valid by using the common forms of valid arguments and fallacies.
If you sneeze with your eyes open, your earlobes shrivel up.
Your earlobes shrivel up.
$\therefore$ You sneeze with your eyes open.

A) Invalid
$\begin{array}{l}
p \rightarrow q \
q\
\hline\therefore p
\end{array}$

B) Valid
$\begin{array}{l}
p \rightarrow q \
\sim q\
\hline\therefore p
\end{array}$

C) Valid
$\begin{array}{l}
p \rightarrow q \
q\
\hline\therefore p
\end{array}$

D) Invalid
$\begin{array}{l}
p \rightarrow q \
\sim q\
\hline\therefore p
\end{array}$

Accepted Answer

The answer of Write the argument in symbols; then decide...

Question 11

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

Accepted Answer

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 
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 12

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.

Accepted Answer

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

Question 13

Which sentence is not a statement?

Accepted Answer

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

Question 14

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

Accepted Answer

A)  Self-contradiction 
B)  Tautology 
C)  Neither 
A)  Self-contradiction 
B)  Tautology 
C)  Neither

Question 15

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

Accepted Answer

A)  Valid 
B)  Invalid 
A)  Valid 
B)  Invalid

Question 16

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

Accepted Answer

A)  Neither 
B)  Negations 
C)  Logically equivalent 
A)  Neither 
B)  Negations 
C)  Logically equivalent

Question 17

$$\begin{array}{l}
\text { Complete the following truth table. }\
\begin{array} { l | l | l | l | l } 
p & q & r & ( r \rightarrow \sim q ) & ( r \rightarrow \sim q ) \vee \sim p \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & & \
\mathrm { T } & \mathrm { T } & \mathrm { F } & & \
\mathrm { T } & \mathrm { F } & \mathrm { T } & & \
\mathrm { T } & \mathrm { F } & \mathrm { F } & & \
\mathrm { F } & \mathrm { T } & \mathrm { T } & & \
\mathrm { F } & \mathrm { T } & \mathrm { F } & & \
\mathrm { F } & \mathrm { F } & \mathrm { T } & & \
\mathrm { F } & \mathrm { F } & \mathrm { F } & &
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Complete the following truth table....

Question 18

Find the inverse of the statement.
$\sim p \rightarrow q$

A) $\sim q \rightarrow p$
B) $q \rightarrow \sim p$
C) $p \rightarrow \sim q$
D) $p \rightarrow q$

Accepted Answer

The answer of Find the inverse of the statement.
\(\sim p...

Question 19

Let $p =$ "Greg is in my history class." Let $q =$ "Lew is in my Spanish class." Write the following statement in words.
$$\sim p \vee \sim q$$

Accepted Answer

Greg is not in my hi

Question 20

Let $p =$ "Jake's favorite is pizza." Let $q =$ "Ian's favorite is hamburgers." Write the following statement in words.
$$\sim p \wedge q$$

Accepted Answer

Jake's favorite is n

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

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.

Let p = "I am hungry." Let q = "I am going to have a snack." Write the following statement in words. $\sim p \wedge ( q \rightarrow p )$

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

Determine the validity of the following argument. \simp\veeq

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

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

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

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.

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

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.

Which sentence is not a statement?

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

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies. \simp\rightarrowq \simr\rightarrowq \therefore\simp\rightarrowr

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

Complete the following truth table. p q r (r\rightarrow\simq) (r\rightarrow\simq)\vee\simp

Find the inverse of the statement. $\sim p \rightarrow q$ A) $\sim q \rightarrow p$ B) $q \rightarrow \sim p$ C) $p \rightarrow \sim q$ D) $p \rightarrow q$

Let $p =$ "Greg is in my history class." Let $q =$ "Lew is in my Spanish class." Write the following statement in words. $\sim p \vee \sim q$

Let $p =$ "Jake's favorite is pizza." Let $q =$ "Ian's favorite is hamburgers." Write the following statement in words. $\sim p \wedge q$

Problem Solving

Set

Numeration Systems

The Real Number System

Topics in Algebra

Consumer Mathematics

Measurement

Geometry

Probability and Counting Techniques

Statistics

Voting Methods

Graph Theory

Available Online: Other Mathematical Systems

Summary

Filters

Exam 3: Logic

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

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.

Let p = "I am hungry." Let q = "I am going to have a snack." Write the following statement in words. ∼p∧(q→p)\sim p \wedge ( q \rightarrow p )∼p∧(q→p)

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

Determine the validity of the following argument. \simp\veeq

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

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

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

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.

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

Determine whether each sentence is a statement or not. i. 2×3=02 \times 3 = 02×3=0 ii. Please don't yell. iii. She went to Spain. iv. Kel studied for hours.

Which sentence is not a statement?

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

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies. \simp\rightarrowq \simr\rightarrowq \therefore\simp\rightarrowr

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

Complete the following truth table. p q r (r\rightarrow\simq) (r\rightarrow\simq)\vee\simp

Find the inverse of the statement. ∼p→q\sim p \rightarrow q∼p→q A) ∼q→p\sim q \rightarrow p∼q→p B) q→∼pq \rightarrow \sim pq→∼p C) p→∼qp \rightarrow \sim qp→∼q D) p→qp \rightarrow qp→q

Let p=p =p= "Greg is in my history class." Let q=q =q= "Lew is in my Spanish class." Write the following statement in words. ∼p∨∼q\sim p \vee \sim q∼p∨∼q

Let p=p =p= "Jake's favorite is pizza." Let q=q =q= "Ian's favorite is hamburgers." Write the following statement in words. ∼p∧q\sim p \wedge q∼p∧q

Problem Solving

Set

Numeration Systems

The Real Number System

Topics in Algebra

Consumer Mathematics

Measurement

Geometry

Probability and Counting Techniques

Statistics

Voting Methods

Graph Theory

Available Online: Other Mathematical Systems

Summary

Filters

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

Let p = "I am hungry." Let q = "I am going to have a snack." Write the following statement in words. $\sim p \wedge ( q \rightarrow p )$

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

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.

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

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

Find the inverse of the statement. $\sim p \rightarrow q$ A) $\sim q \rightarrow p$ B) $q \rightarrow \sim p$ C) $p \rightarrow \sim q$ D) $p \rightarrow q$

Let $p =$ "Greg is in my history class." Let $q =$ "Lew is in my Spanish class." Write the following statement in words. $\sim p \vee \sim q$

Let $p =$ "Jake's favorite is pizza." Let $q =$ "Ian's favorite is hamburgers." Write the following statement in words. $\sim p \wedge q$