Question 1

Write a negation of the inequality. Do not use a slash symbol.
-$x \geq - 50$

Accepted Answer

A)  $x \geq 50$ 
B)  $x < 50$ 
C)  $x < - 50$ 
D)  $x \leq - 50$ 
A)  $x \geq 50$ 
B)  $x < 50$ 
C)  $x < - 50$ 
D)  $x \leq - 50$

Question 2

Find the truth value of the statement.
-$7 - 5 = 2 \text { if and only if } 11 + 2 = 14$

Accepted Answer

A) True 
 B)False

Question 3

Tell whether the conditional statement is true or false.
-Here F represents a false statement. $\mathrm { F } \rightarrow ( 5 = 8 )$

Accepted Answer

A) True 
 B)False

Question 4

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

Accepted Answer

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

Question 5

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$
-If $7 x + 2 y > 6$, the answer is "Sea."

Accepted Answer

A)  $7 x + 2 y > - 6$ so the answer is not "Sea." 
B)  $7 x + 2 y \leq 6$ and the answer is not "Sea." 
C)  If $7 x + 2 y > 6$, the answer is not "Sea." 
D)  $7 x + 2 y > 6$ and the answer is not "Sea." 
A)  $7 x + 2 y > - 6$ so the answer is not "Sea." 
B)  $7 x + 2 y \leq 6$ and the answer is not "Sea." 
C)  If $7 x + 2 y > 6$, the answer is not "Sea." 
D)  $7 x + 2 y > 6$ and the answer is not "Sea."

Question 6

Solve the logic puzzle by using a grid.
-The scores of a math test for five students were posted on the bulletin board. The students' names are Tom, Penny, Jim, John and Fred. Tom and Fred scored the same number of points. Penny did
Not get the highest score. John's score was 5 points lower than Jim's. The scores were 69, 52, 94, 52 And 89. Which student received what score?

Accepted Answer

A)  Tom and Fred 52, Penny 69, Jim 94, John 89 
B)  Tom and Fred 52, Penny 89, Jim 69, John 94 
C)  Tom and Jim 52, Penny 89, Fred 69, John 94 
D)  Tom and Jim 52, John 69, Jim 89, Penny 94 
A)  Tom and Fred 52, Penny 69, Jim 94, John 89 
B)  Tom and Fred 52, Penny 89, Jim 69, John 94 
C)  Tom and Jim 52, Penny 89, Fred 69, John 94 
D)  Tom and Jim 52, John 69, Jim 89, Penny 94

Question 7

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both".
-$8 + 4 = 20 \underline\vee 3 + 5 = 13$

Accepted Answer

A) True 
 B)False

Question 8

Construct a truth table for the statement.
-$(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

Accepted Answer

A) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S} \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
D) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T}
\end{array}$ 
A) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S} \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{S} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{S}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
D) 
$\begin{array}{lll}
\mathrm{r} & \mathrm{s} & (\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T}
\end{array}$

Question 9

Write a logical statement representing the following circuit. Simplify when possible.
-$\sim p \rightarrow [ ( q \wedge r ) \vee \sim p ]$

Accepted Answer

The statem

Question 10

Decide whether the statement is compound.
-I'll go to Mexico or Costa Rica for my next vacation.

Accepted Answer

A) Compound 
B) Not compound 
A) Compound 
B) Not compound

Question 11

$$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$$
-$\sim ( p \wedge q )$

Accepted Answer

A) True 
 B)False

Question 12

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If it is cold, then you need a coat.
$\underline { \text {You do not need a coat} }$
It is not cold.

Accepted Answer

A)  Valid by reasoning of transitivity 
B)  Valid by modus tollens 
C)  Fallacy by fallacy of the converse 
D)  Fallacy by fallacy of the inverse 
A)  Valid by reasoning of transitivity 
B)  Valid by modus tollens 
C)  Fallacy by fallacy of the converse 
D)  Fallacy by fallacy of the inverse

Question 13

Determine whether the argument is valid or invalid.
-If you are infected with the measles, then it can be transmitted. The results are grave and it cannot be transmitted. Therefore, if the results are not grave, then you are infected with the measles

Accepted Answer

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

Question 14

$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$

Accepted Answer

A) True 
 B)False

Question 15

$$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$$
-$\sim q \wedge \sim r$

Accepted Answer

A) True 
 B)False

Question 16

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If it's Tuesday, then this must be Paris.
$\underline { \text {Today is Wednesday.} }$
This cannot be Paris.

Accepted Answer

A)  Fallacy by fallacy of the inverse 
B)  Fallacy by fallacy of the converse 
C)  Valid by reasoning of transitivity 
D)  Valid by modus tollens 
A)  Fallacy by fallacy of the inverse 
B)  Fallacy by fallacy of the converse 
C)  Valid by reasoning of transitivity 
D)  Valid by modus tollens

Question 17

Solve the Sudoku.
-Hard $$\begin{array} { | l | l | l | l | l | l | l | l | l | } 
\hline & 8 & & & & 6 & 7 & & 5 \
\hline & & & & 9 & & & 8 & \
\hline 3 & & & & 8 & & & & \
\hline 9 & & 5 & & & & 2 & & \
\hline & 3 & & 9 & 6 & 1 & & 5 & \
\hline & & 4 & & & & 9 & & 8 \
\hline & & & & 3 & & & & 2 \
\hline & 6 & & & 7 & & & & \
\hline 7 & & 9 & 6 & & & & 3 & \
\hline
\end{array}$$

Accepted Answer

\[\begin{array} { | l | l | l | l | l |

Question 18

Tell whether the conditional statement is true or false.
-$( 8 = 12 - 4 ) \rightarrow ( 5 > 0 )$

Accepted Answer

A) True 
 B)False

Question 19

Tell whether the conditional statement is true or false.
-Here F represents a false statement. $( 2 = 2 ) \rightarrow F$

Accepted Answer

A) True 
 B)False

Question 20

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
-$\sim \mathrm { p} \vee ( \mathrm {~q} \wedge \sim \mathrm { r } )$

Accepted Answer

A) True 
 B)False

Write a negation of the inequality. Do not use a slash symbol. - $x \geq - 50$

Find the truth value of the statement. - $7 - 5 = 2 \text { if and only if } 11 + 2 = 14$

Tell whether the conditional statement is true or false. -Here F represents a false statement. $\mathrm { F } \rightarrow ( 5 = 8 )$

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If $7 x + 2 y > 6$ , the answer is "Sea."

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both". - $8 + 4 = 20 \underline\vee 3 + 5 = 13$

Construct a truth table for the statement. - $(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

Write a logical statement representing the following circuit. Simplify when possible. - $\sim p \rightarrow [ ( q \wedge r ) \vee \sim p ]$

Decide whether the statement is compound. -I'll go to Mexico or Costa Rica for my next vacation.

$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$ - $\sim ( p \wedge q )$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it is cold, then you need a coat. $\underline { \text {You do not need a coat} }$ It is not cold.

Determine whether the argument is valid or invalid. -If you are infected with the measles, then it can be transmitted. The results are grave and it cannot be transmitted. Therefore, if the results are not grave, then you are infected with the measles

$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$

$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$ - $\sim q \wedge \sim r$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it's Tuesday, then this must be Paris. $\underline { \text {Today is Wednesday.} }$ This cannot be Paris.

Solve the Sudoku. -Hard 8 6 7 5 9 8 3 8 9 5 2 3 9 6 1 5 4 9 8 3 2 6 7 7 9 6 3

Tell whether the conditional statement is true or false. - $( 8 = 12 - 4 ) \rightarrow ( 5 > 0 )$

Tell whether the conditional statement is true or false. -Here F represents a false statement. $( 2 = 2 ) \rightarrow F$

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim \mathrm { p} \vee ( \mathrm {~q} \wedge \sim \mathrm { r } )$

The Art of Problem Solving

The Basic Concepts of Set Theory

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 3: Introduction to Logic

Write a negation of the inequality. Do not use a slash symbol. - x≥−50x \geq - 50x≥−50

Find the truth value of the statement. - 7−5=2 if and only if 11+2=147 - 5 = 2 \text { if and only if } 11 + 2 = 147−5=2 if and only if 11+2=14

Tell whether the conditional statement is true or false. -Here F represents a false statement. F→(5=8)\mathrm { F } \rightarrow ( 5 = 8 )F→(5=8)

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.

Decide whether the compound statement is true or false. The symbol for exclusive disjunction ∨\vee∨ represents "one or the other is true, but not both". - 8+4=20∨‾3+5=138 + 4 = 20 \underline\vee 3 + 5 = 138+4=20∨​3+5=13

Construct a truth table for the statement. - (r→∼s)→(r∧∼s)(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})(r→∼s)→(r∧∼s)

Write a logical statement representing the following circuit. Simplify when possible. - ∼p→[(q∧r)∨∼p]\sim p \rightarrow [ ( q \wedge r ) \vee \sim p ]∼p→[(q∧r)∨∼p]

Decide whether the statement is compound. -I'll go to Mexico or Costa Rica for my next vacation.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it is cold, then you need a coat. You do not need a coat‾\underline { \text {You do not need a coat} }You do not need a coat​ It is not cold.

Determine whether the argument is valid or invalid. -If you are infected with the measles, then it can be transmitted. The results are grave and it cannot be transmitted. Therefore, if the results are not grave, then you are infected with the measles

If p is false then the statement q→(∼p∨q) must be true. \text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. } If p is false then the statement q→(∼p∨q) must be true.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it's Tuesday, then this must be Paris. Today is Wednesday.‾\underline { \text {Today is Wednesday.} }Today is Wednesday.​ This cannot be Paris.

Solve the Sudoku. -Hard 8 6 7 5 9 8 3 8 9 5 2 3 9 6 1 5 4 9 8 3 2 6 7 7 9 6 3

Tell whether the conditional statement is true or false. - (8=12−4)→(5>0)( 8 = 12 - 4 ) \rightarrow ( 5 > 0 )(8=12−4)→(5>0)

Tell whether the conditional statement is true or false. -Here F represents a false statement. (2=2)→F( 2 = 2 ) \rightarrow F(2=2)→F

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - ∼p∨( q∧∼r)\sim \mathrm { p} \vee ( \mathrm {~q} \wedge \sim \mathrm { r } )∼p∨( q∧∼r)

The Art of Problem Solving

The Basic Concepts of Set Theory

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Write a negation of the inequality. Do not use a slash symbol. - $x \geq - 50$

Find the truth value of the statement. - $7 - 5 = 2 \text { if and only if } 11 + 2 = 14$

Tell whether the conditional statement is true or false. -Here F represents a false statement. $\mathrm { F } \rightarrow ( 5 = 8 )$

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both". - $8 + 4 = 20 \underline\vee 3 + 5 = 13$

Construct a truth table for the statement. - $(\mathrm{r} \rightarrow \sim \mathrm{s}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s})$

Write a logical statement representing the following circuit. Simplify when possible. - $\sim p \rightarrow [ ( q \wedge r ) \vee \sim p ]$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it is cold, then you need a coat. $\underline { \text {You do not need a coat} }$ It is not cold.

$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it's Tuesday, then this must be Paris. $\underline { \text {Today is Wednesday.} }$ This cannot be Paris.

Tell whether the conditional statement is true or false. - $( 8 = 12 - 4 ) \rightarrow ( 5 > 0 )$

Tell whether the conditional statement is true or false. -Here F represents a false statement. $( 2 = 2 ) \rightarrow F$

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim \mathrm { p} \vee ( \mathrm {~q} \wedge \sim \mathrm { r } )$