Question 1

Determine whether the argument is valid or invalid.
-All women are wealthy. Amanda is a woman. Therefore, Amanda is wealthy.

Accepted Answer

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

Question 2

Given p is true, q is true, and r is false, find the truth value of the statement.
-$\sim r \rightarrow \sim p$

Accepted Answer

A) True 
 B)False

Question 3

Decide whether the statement is compound.
-The sign read "Not for sale".

Accepted Answer

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

Question 4

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement.
-$\mathrm { p } \vee \sim \mathrm { q }$

Accepted Answer

A) True 
 B)False

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 the package is in the mail, then it should be here by Tuesday.

Accepted Answer

A) If the package is in the mail, then it will not be here by Tuesday. 
B) The package is in the mail so it should be here by Tuesday. 
C) The package is in the mail and will not be here by Tuesday. 
D) The package is not in the mail and will not be here by Tuesday. 
A) If the package is in the mail, then it will not be here by Tuesday. 
B) The package is in the mail so it should be here by Tuesday. 
C) The package is in the mail and will not be here by Tuesday. 
D) The package is not in the mail and will not be here by Tuesday.

Question 6

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

Accepted Answer

The answer of Write a logical statement representing the following...

Question 7

Solve the logic puzzle by using a grid.
-Susan, Tim, Peter, Lucy and Norma have 20 pieces of candy to share. Susan only wants two pieces. Peter will take as many as he can. Tim and Lucy will end up with the same number of pieces.
Norma will not get the most pieces, but Susan will get the least pieces. Norma will get twice as
Many pieces as Susan and the same number as Tim. They all end up with an even number of pieces And no one has more than 10 pieces. How many pieces of candy does each get.

Accepted Answer

A)  Susan $\rightarrow 2$, Tim $\rightarrow 2$, Peter $\rightarrow 10$, Lucy $\rightarrow 4$, Norma $\rightarrow 2$ 
B)  Susan $\rightarrow 2$, Tim $\rightarrow 4$, Peter $\rightarrow 8$, Lucy $\rightarrow 2$, Norma $\rightarrow 4$ 
C)  Susan $\rightarrow 2$, Tim $\rightarrow 4$, Peter $\rightarrow 6$, Lucy $\rightarrow 4$, Norma $\rightarrow 4$ 
D)  Susan $\rightarrow 2$, Tim $\rightarrow 2$, Peter $\rightarrow 8$, Lucy $\rightarrow 4$, Norma $\rightarrow 4$ 
A)  Susan $\rightarrow 2$, Tim $\rightarrow 2$, Peter $\rightarrow 10$, Lucy $\rightarrow 4$, Norma $\rightarrow 2$ 
B)  Susan $\rightarrow 2$, Tim $\rightarrow 4$, Peter $\rightarrow 8$, Lucy $\rightarrow 2$, Norma $\rightarrow 4$ 
C)  Susan $\rightarrow 2$, Tim $\rightarrow 4$, Peter $\rightarrow 6$, Lucy $\rightarrow 4$, Norma $\rightarrow 4$ 
D)  Susan $\rightarrow 2$, Tim $\rightarrow 2$, Peter $\rightarrow 8$, Lucy $\rightarrow 4$, Norma $\rightarrow 4$

Question 8

Write the compound statement in symbols. Let $r =$ "The food is good."
$\begin{array} { l } 
p = \text { "I eat too much." } \
q = \text { "I'll exercise." }
\end{array}$
-I'll exercise if I don't eat too much.

Accepted Answer

A)  $\sim p \wedge q$ 
B)  $\sim p \rightarrow q$ 
C)  $\sim p \vee q$ 
D)  $\sim ( p \rightarrow q )$ 
A)  $\sim p \wedge q$ 
B)  $\sim p \rightarrow q$ 
C)  $\sim p \vee q$ 
D)  $\sim ( p \rightarrow q )$

Question 9

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

Accepted Answer

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

Question 10

Write the converse, inverse, or contrapositive of the statement as requested.
-All cats catch birds. Inverse

Accepted Answer

A) If it doesn't catch birds, it's not a cat. 
B) Not all cats catch birds. 
C) If it's not a cat, it doesn't catch birds. 
D) If it catches birds, it's a cat. 
A) If it doesn't catch birds, it's not a cat. 
B) Not all cats catch birds. 
C) If it's not a cat, it doesn't catch birds. 
D) If it catches birds, it's a cat.

Question 11

Write a logical statement representing the following circuit. Simplify when possible.
-

Accepted Answer

The answer of Write a logical statement representing the following...

Question 12

Decide whether the statement is true or false.
-For every real number r, r  6.

Accepted Answer

A) True 
 B)False

Question 13

Tell whether the conditional statement is true or false.
-Here T represents a true statement. $( 6 \neq 2 + 4 ) \rightarrow \mathrm { T }$

Accepted Answer

A) True 
 B)False

Question 14

Give the number of rows in the truth table for the compound statement.
-$\sim ( p \wedge q ) \wedge ( w \wedge \sim s ) \vee ( r \vee t ) \wedge ( \sim u \wedge s )$

Accepted Answer

A) 128 
B) 64 
C) 256 
D) 16 
A) 128 
B) 64 
C) 256 
D) 16

Question 15

Use De Morgan's laws to write the negation of the statement.
-It is Saturday and it is not raining.

Accepted Answer

A) It is not Saturday or it is not raining. 
B) It is not Saturday and it is raining. 
C) It is not Saturday or it is raining. 
D) It is Saturday and it is raining. 
A) It is not Saturday or it is not raining. 
B) It is not Saturday and it is raining. 
C) It is not Saturday or it is raining. 
D) It is Saturday and it is raining.

Question 16

Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$
-If the sun comes out Tuesday, the daisies will open.

Accepted Answer

A) The sun does not come out Tuesday or the daisies will open. 
B) The sun does not come out Tuesday or the daisies will not open. 
C) The sun does not come out Tuesday but the daisies will not open. 
D) The sun comes out Tuesday and the daisies will not open. 
A) The sun does not come out Tuesday or the daisies will open. 
B) The sun does not come out Tuesday or the daisies will not open. 
C) The sun does not come out Tuesday but the daisies will not open. 
D) The sun comes out Tuesday and the daisies will not open.

Question 17

Write the compound statement in words. Let $r =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$q =$ "His owners are happy."
-$( r \wedge p ) \rightarrow q$

Accepted Answer

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

Question 18

Construct a truth table for the statement.
-$\sim p \rightarrow(\sim p \wedge \wedge q)$

Accepted Answer

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

Question 19

Write the converse, inverse, or contrapositive of the statement as requested.
-$\sim \mathrm { q } \rightarrow \sim \mathrm { p }$
Converse

Accepted Answer

A)  $q \rightarrow p$ 
B)  $\sim ( q \rightarrow p )$ 
C)  $\sim \mathrm { p } \rightarrow \sim \mathrm { q }$ 
D)  $\mathrm { p } \rightarrow \mathrm { q }$ 
A)  $q \rightarrow p$ 
B)  $\sim ( q \rightarrow p )$ 
C)  $\sim \mathrm { p } \rightarrow \sim \mathrm { q }$ 
D)  $\mathrm { p } \rightarrow \mathrm { q }$

Question 20

Use De Morgan's laws to write the negation of the statement.
-Roger or Emil will attend the game.

Accepted Answer

A) Roger will not attend the game and Emil will attend the game. 
B) Roger will not attend the game and Emil will not attend the game. 
C) Roger and Emil will attend the game. 
D) Roger or Emil will not attend the game. 
A) Roger will not attend the game and Emil will attend the game. 
B) Roger will not attend the game and Emil will not attend the game. 
C) Roger and Emil will attend the game. 
D) Roger or Emil will not attend the game.

Determine whether the argument is valid or invalid. -All women are wealthy. Amanda is a woman. Therefore, Amanda is wealthy.

Given p is true, q is true, and r is false, find the truth value of the statement. - $\sim r \rightarrow \sim p$

Decide whether the statement is compound. -The sign read "Not for sale".

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - $\mathrm { p } \vee \sim \mathrm { q }$

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If the package is in the mail, then it should be here by Tuesday.

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

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -I'll exercise if I don't eat too much.

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

Write the converse, inverse, or contrapositive of the statement as requested. -All cats catch birds. Inverse

Write a logical statement representing the following circuit. Simplify when possible. -

Decide whether the statement is true or false. -For every real number r, r < 7 or r > 6.

Tell whether the conditional statement is true or false. -Here T represents a true statement. $( 6 \neq 2 + 4 ) \rightarrow \mathrm { T }$

Give the number of rows in the truth table for the compound statement. - $\sim ( p \wedge q ) \wedge ( w \wedge \sim s ) \vee ( r \vee t ) \wedge ( \sim u \wedge s )$

Use De Morgan's laws to write the negation of the statement. -It is Saturday and it is not raining.

Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$ -If the sun comes out Tuesday, the daisies will open.

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $( r \wedge p ) \rightarrow q$

Construct a truth table for the statement. - $\sim p \rightarrow(\sim p \wedge \wedge q)$

Write the converse, inverse, or contrapositive of the statement as requested. - $\sim \mathrm { q } \rightarrow \sim \mathrm { p }$ Converse

Use De Morgan's laws to write the negation of the statement. -Roger or Emil will attend the game.

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

Determine whether the argument is valid or invalid. -All women are wealthy. Amanda is a woman. Therefore, Amanda is wealthy.

Given p is true, q is true, and r is false, find the truth value of the statement. - ∼r→∼p\sim r \rightarrow \sim p∼r→∼p

Decide whether the statement is compound. -The sign read "Not for sale".

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - p∨∼q\mathrm { p } \vee \sim \mathrm { q }p∨∼q

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

Write the compound statement in symbols. Let r=r =r= "The food is good." p= "I eat too much." q= "I'll exercise." -I'll exercise if I don't eat too much.

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

Write the converse, inverse, or contrapositive of the statement as requested. -All cats catch birds. Inverse

Write a logical statement representing the following circuit. Simplify when possible. -

Decide whether the statement is true or false. -For every real number r, r < 7 or r > 6.

Tell whether the conditional statement is true or false. -Here T represents a true statement. (6≠2+4)→T( 6 \neq 2 + 4 ) \rightarrow \mathrm { T }(6=2+4)→T

Give the number of rows in the truth table for the compound statement. - ∼(p∧q)∧(w∧∼s)∨(r∨t)∧(∼u∧s)\sim ( p \wedge q ) \wedge ( w \wedge \sim s ) \vee ( r \vee t ) \wedge ( \sim u \wedge s )∼(p∧q)∧(w∧∼s)∨(r∨t)∧(∼u∧s)

Use De Morgan's laws to write the negation of the statement. -It is Saturday and it is not raining.

Write the compound statement in words. Let r=r =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=q =q= "His owners are happy." - (r∧p)→q( r \wedge p ) \rightarrow q(r∧p)→q

Construct a truth table for the statement. - ∼p→(∼p∧∧q)\sim p \rightarrow(\sim p \wedge \wedge q)∼p→(∼p∧∧q)

Write the converse, inverse, or contrapositive of the statement as requested. - ∼q→∼p\sim \mathrm { q } \rightarrow \sim \mathrm { p }∼q→∼p Converse

Use De Morgan's laws to write the negation of the statement. -Roger or Emil will attend the game.

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

Given p is true, q is true, and r is false, find the truth value of the statement. - $\sim r \rightarrow \sim p$

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - $\mathrm { p } \vee \sim \mathrm { q }$

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

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -I'll exercise if I don't eat too much.

Tell whether the conditional statement is true or false. -Here T represents a true statement. $( 6 \neq 2 + 4 ) \rightarrow \mathrm { T }$

Give the number of rows in the truth table for the compound statement. - $\sim ( p \wedge q ) \wedge ( w \wedge \sim s ) \vee ( r \vee t ) \wedge ( \sim u \wedge s )$

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $( r \wedge p ) \rightarrow q$

Construct a truth table for the statement. - $\sim p \rightarrow(\sim p \wedge \wedge q)$

Write the converse, inverse, or contrapositive of the statement as requested. - $\sim \mathrm { q } \rightarrow \sim \mathrm { p }$ Converse