Question 1

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

Accepted Answer

$\begin{array}{c|c|c|c|c}
p & q & r & (r \rightarrow \sim q) & (r \rightarrow \sim q) \vee \sim p \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T}
\end{array}$

Question 2

Use a truth table to determine whether the argument is valid.
$\begin{array}{l}
\sim p \wedge q \
\frac{r \rightarrow \sim q}{\therefore r}
\end{array}$

Accepted Answer

$$\text { The argument is not valid. }$$
$\begin{array}{c|c|c|c|c|c|c}
p & q & r & (\sim p \wedge q) & (r \rightarrow \sim q) & (\sim p \wedge q) \wedge(r \rightarrow \sim q) & {[(\sim p \wedge q) \wedge(r \rightarrow \sim q}) \
& & & & && \Rightarrow r \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T}
\end{array}$

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.

Accepted Answer

A simple statement is one that does not contain any other statement as a part. "February is the shortest month" is a simple statement because it is a single, declarative sentence without any conjunctions or conditions.

Question 4

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

Accepted Answer

The answer of Let p = "Sally is three years...

Question 5

Complete a truth table for the following statement.
$(r \wedge q) \vee(\sim p \wedge q)$

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

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

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

Accepted Answer

The answer of Complete a truth table for the following...

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

Accepted Answer

A question is not a statement.

Question 7

Identify $p , q$, and $r$. Then translate the argument into symbols and determine whether it is valid or invalid. If I lose ten pounds, then my tux will fit. If my tux fits, then I will go to the reunion. $\therefore$ If I lose ten pounds, then I will go to the reunion.

Accepted Answer

The answer of Identify $p , q$, and $r$. Then...

Question 8

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

Accepted Answer

The answer of Let p = "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.

Accepted Answer

The answer of Let p = "Daphne speaks Spanish." Let...

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.

Accepted Answer

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

Question 11

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

Accepted Answer

The answer of Decide if the statement is simple or...

Question 12

Use a truth table to determine whether the argument is valid.
$$\begin{array} { l } 
p \wedge q \
\sim p \vee \sim q \
\hline \therefore \sim p
\end{array}$$

Accepted Answer

The answer of Use a truth table to determine whether...

Question 13

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

Accepted Answer

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

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.

Accepted Answer

The answer of Let p = "Paolo bicycles to school."...

Question 15

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

Accepted Answer

The answer of Draw an Euler circle diagram for the...

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.

Accepted Answer

The answer of Let p = "Paolo bicycles to school."...

Question 17

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

Accepted Answer

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

Question 18

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist.
ii. She is not feeling well.
iii. $7 + 2 = 14$
iv. He is taking history and economics.

Accepted Answer

The answer of Decide whether each statement is simple or...

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

The answer of Let $p =$ "Greg is in my...

Question 20

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

The answer of Let p = "Sally is three years...

Quiz 3: Logic

Use a truth table to determine whether the argument is valid. $\begin{array}{l}\sim p \wedge q \\\frac{r \rightarrow \sim q}{\therefore r}\end{array}$

Which of the following is a simple statement?

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

Which sentence is not a statement?

Identify $p , q$ , and $r$ . Then translate the argument into symbols and determine whether it is valid or invalid. If I lose ten pounds, then my tux will fit. If my tux fits, then I will go to the reunion. $\therefore$ If I lose ten pounds, then I will go to the reunion.

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

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.

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.

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

Use a truth table to determine whether the argument is valid. $\begin{array} { l } p \wedge q \\\sim p \vee \sim q \\\hline \therefore \sim p\end{array}$

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.

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

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.

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. $7 + 2 = 14$ iv. He is taking history and economics.

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

Quiz 3: Logic

Use a truth table to determine whether the argument is valid. ∼p∧qr→∼q∴r\begin{array}{l}\sim p \wedge q \\\frac{r \rightarrow \sim q}{\therefore r}\end{array}∼p∧q∴rr→∼q​​

Which of the following is a simple statement?

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

Which sentence is not a statement?

Identify p,qp , qp,q , and rrr . Then translate the argument into symbols and determine whether it is valid or invalid. If I lose ten pounds, then my tux will fit. If my tux fits, then I will go to the reunion. ∴\therefore∴ If I lose ten pounds, then I will go to the reunion.

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

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.

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.

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

Use a truth table to determine whether the argument is valid. p∧q∼p∨∼q∴∼p\begin{array} { l } p \wedge q \\\sim p \vee \sim q \\\hline \therefore \sim p\end{array}p∧q∼p∨∼q∴∼p​​

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.

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

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.

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. 7+2=147 + 2 = 147+2=14 iv. He is taking history and economics.

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

Use a truth table to determine whether the argument is valid. $\begin{array}{l}\sim p \wedge q \\\frac{r \rightarrow \sim q}{\therefore r}\end{array}$

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

Identify $p , q$ , and $r$ . Then translate the argument into symbols and determine whether it is valid or invalid. If I lose ten pounds, then my tux will fit. If my tux fits, then I will go to the reunion. $\therefore$ If I lose ten pounds, then I will go to the reunion.

Use a truth table to determine whether the argument is valid. $\begin{array} { l } p \wedge q \\\sim p \vee \sim q \\\hline \therefore \sim p\end{array}$

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. $7 + 2 = 14$ iv. He is taking history and economics.

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