Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided.
-  
It is false that 18% of people watch 8 hours of TV per week and 45% watch 7 hours of TV per week.

Accepted Answer

A) True 
 B)False

Question 5

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement.
-9 - 2 = 7 if and only if 10 + 4 = 15.

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A)  All athletes are musicians. 
B)  All athletes are not musicians. 
C)  Some athletes are not musicians. 
D)  No 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 7

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

Accepted Answer

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. 
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 8

Construct a truth table for the statement.
-$\sim \mathrm { r } \wedge \sim \mathrm { q }$

Accepted Answer

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

Question 9

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$$\sim ( \mathrm { p } \vee \mathrm { q } ) \rightarrow \mathrm { r } , ( \sim \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow \mathrm { r }$$

Accepted Answer

A)  Equivalent 
B)  Not equivalent 
A)  Equivalent 
B)  Not equivalent

Question 10

Identify the standard form of the argument.
-$$\begin{array} { l } 
\mathrm { p } \vee \mathrm { q } \
\sim \mathrm { p } \
\hline \therefore \mathrm { q }
\end{array}$$

Accepted Answer

A)  Fallacy of the Converse 
B)  Fallacy of the Inverse 
C)  Law of Syllogism 
D)  Disjunctive Syllogism 
A)  Fallacy of the Converse 
B)  Fallacy of the Inverse 
C)  Law of Syllogism 
D)  Disjunctive Syllogism

Question 11

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$[ ( p \vee q ) \vee r ] \rightarrow [ \sim r \wedge ( p \wedge q ) ]$$

Accepted Answer

A)  Tautology 
B)  Self-contradiction 
C)  Implication 
D)  None of these 
A)  Tautology 
B)  Self-contradiction 
C)  Implication 
D)  None of these

Question 12

Construct a truth table for the statement.
-$\sim[p \leftrightarrow(\sim q)]$

Accepted Answer

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

Question 13

Write the indicated statement. Use De Morgan's Laws if necessary.
-If it is a cat, then it catches birds.
Inverse

Accepted Answer

A)  If it doesnʹt catch birds, itʹs not a cat. 
B)  If itʹs not a cat, it doesnʹt catch birds. 
C)  Not all cats catch birds. 
D)  If it catches birds, itʹs a cat. 
A)  If it doesnʹt catch birds, itʹs not a cat. 
B)  If itʹs not a cat, it doesnʹt catch birds. 
C)  Not all cats catch birds. 
D)  If it catches birds, itʹs a cat.

Question 14

Convert the compound statement into words.
-$$\begin{array} { l } 
\mathrm { p } = \text { "Students are happy." } \
\mathrm { q } = \text { "Teachers are happy." } \
\sim \left( \mathrm { p } _ { \vee } \sim \mathrm { q } \right)
\end{array}$$

Accepted Answer

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. 
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 15

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

Accepted Answer

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. 
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 16

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false.
-If the sum of the interior angles of a polygon does not measure 180°, then the polygon is not a Triangle.

Accepted Answer

A)  If the polygon is a triangle, then the sum of the interior angles of the polygon measures 180°. true 
B)  If the polygon is not a triangle, then the sum of the interior angles of the polygon do not measure 180°. true 
C)  If the polygon is not a triangle, then the sum of the interior angles of the polygon do not measure 180°. false 
D)  If the polygon is a triangle, then the sum of the interior angles of the polygon measures 180°. false 
A)  If the polygon is a triangle, then the sum of the interior angles of the polygon measures 180°. true 
B)  If the polygon is not a triangle, then the sum of the interior angles of the polygon do not measure 180°. true 
C)  If the polygon is not a triangle, then the sum of the interior angles of the polygon do not measure 180°. false 
D)  If the polygon is a triangle, then the sum of the interior angles of the polygon measures 180°. false

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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.

Accepted Answer

A)  (r ∧ p) → q 
B) r ∧ (p → q) 
C)  (r ∨ p) → q 
D) (r → p) ∨ q 
A)  (r ∧ p) → q 
B) r ∧ (p → q) 
C)  (r ∨ p) → q 
D) (r → p) ∨ q

Question 19

Write an equivalent sentence for the statement.
-Denim is not out and linen is not in. (Hint: Use De Morganʹs laws.)

Accepted Answer

A)  It is not the case that denim is out and linen is in. 
B)  It is not the case that denim is in or linen is out. 
C)  It is not the case that denim is out or linen is in. 
D)  Denim and linen are in. 
A)  It is not the case that denim is out and linen is in. 
B)  It is not the case that denim is in or linen is out. 
C)  It is not the case that denim is out or linen is in. 
D)  Denim and linen are in.

Question 20

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided.
-0 > -7 and 6 ≥ 10

Accepted Answer

A) True 
 B)False

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

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

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

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. - It is false that 18% of people watch 8 hours of TV per week and 45% watch 7 hours of TV per week.

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -9 - 2 = 7 if and only if 10 + 4 = 15.

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

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

Construct a truth table for the statement. - $\sim \mathrm { r } \wedge \sim \mathrm { q }$

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $\sim ( \mathrm { p } \vee \mathrm { q } ) \rightarrow \mathrm { r } , ( \sim \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow \mathrm { r }$

Identify the standard form of the argument. - \vee \sim \therefore

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $[ ( p \vee q ) \vee r ] \rightarrow [ \sim r \wedge ( p \wedge q ) ]$

Construct a truth table for the statement. - $\sim[p \leftrightarrow(\sim q)]$

Write the indicated statement. Use De Morgan's Laws if necessary. -If it is a cat, then it catches birds. Inverse

Convert the compound statement into words. - = "Students are happy." = "Teachers are happy." \sim \sim

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

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. -If the sum of the interior angles of a polygon does not measure 180°, then the polygon is not a Triangle.

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

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.

Write an equivalent sentence for the statement. -Denim is not out and linen is not in. (Hint: Use De Morganʹs laws.)

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -0 > -7 and 6 ≥ 10

Critical Thinking Skills

Sets

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Exam 3: Logic

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 [ ( \sim p \wedge q ) \vee r ]∼[(∼p∧q)∨r]

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

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

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. - It is false that 18% of people watch 8 hours of TV per week and 45% watch 7 hours of TV per week.

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -9 - 2 = 7 if and only if 10 + 4 = 15.

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

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

Construct a truth table for the statement. - ∼r∧∼q\sim \mathrm { r } \wedge \sim \mathrm { q }∼r∧∼q

Identify the standard form of the argument. - \vee \sim \therefore

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - [(p∨q)∨r]→[∼r∧(p∧q)][ ( p \vee q ) \vee r ] \rightarrow [ \sim r \wedge ( p \wedge q ) ][(p∨q)∨r]→[∼r∧(p∧q)]

Construct a truth table for the statement. - ∼[p↔(∼q)]\sim[p \leftrightarrow(\sim q)]∼[p↔(∼q)]

Write the indicated statement. Use De Morgan's Laws if necessary. -If it is a cat, then it catches birds. Inverse

Convert the compound statement into words. - = "Students are happy." = "Teachers are happy." \sim \sim

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

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. -If the sum of the interior angles of a polygon does not measure 180°, then the polygon is not a Triangle.

Given p is true, q is true, and r is false, find the truth value of the statement. - (q∧∼r)→(∼p∨r)( q \wedge \sim r ) \rightarrow ( \sim p \vee r )(q∧∼r)→(∼p∨r)

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.

Write an equivalent sentence for the statement. -Denim is not out and linen is not in. (Hint: Use De Morganʹs laws.)

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -0 > -7 and 6 ≥ 10

Critical Thinking Skills

Sets

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

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

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

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

Construct a truth table for the statement. - $\sim \mathrm { r } \wedge \sim \mathrm { q }$

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $[ ( p \vee q ) \vee r ] \rightarrow [ \sim r \wedge ( p \wedge q ) ]$

Construct a truth table for the statement. - $\sim[p \leftrightarrow(\sim q)]$

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

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