Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

When using a truth table, the statement $\sim \mathrm { p } \vee \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \wedge \mathrm { q } )$.

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

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

Question 6

The argument has a true conclusion. Identify the argument as valid or invalid.
-Eric is older than Camille.
$\underline { \text {Camille is older than Todd.} }$
Todd is younger than Eric.

Accepted Answer

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

Question 7

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

Accepted Answer

A) 
$\begin{array}{ccccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) & \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{lcccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{ccccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
D) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
A) 
$\begin{array}{ccccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) & \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{lcccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{ccccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
D) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{s} & \mathrm{t} & \sim(\mathrm{p} \wedge \mathrm{s}) \rightarrow(\mathrm{p} \rightarrow(\sim \mathrm{t} \wedge \mathrm{s})) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$

Question 8

Decide whether the statement is true or false.
-$\text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. }$

Accepted Answer

A) True 
 B)False

Question 9

Construct a truth table for the statement.
-$\sim(s \vee t) \wedge \sim(t \wedge s)$

Accepted Answer

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

Question 10

Determine whether the argument is valid or invalid.
-The Rams will be in the playoffs if and only if Ozzie is an all-star. Mark loves the Rams or Ozzie is an all-star. Mark does not love the Rams. Therefore, the Rams will not be in the playoffs.

Accepted Answer

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

Question 11

$$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } p \rightarrow q \text {. }$$

Accepted Answer

A) True 
 B)False

Question 12

$$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } \sim p \rightarrow q \text {. }$$

Accepted Answer

A) True 
 B)False

Question 13

Write a negation of the inequality. Do not use a slash symbol.
-$x < 5$

Accepted Answer

A)  $x  5$ 
C)  $x = 5$ 
D)  $x \geq 5$ 
A)  $x  5$ 
C)  $x = 5$ 
D)  $x \geq 5$

Question 14

Decide whether the statement is true or false.
-$\text { For no real number } \mathrm { y } , \mathrm { y }  12 \text {. }$

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

@#LAT-DLM& Draw a circuit repr

Question 16

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-All birds have wings. None of my pets are birds. All animals with wings can flap them.

Accepted Answer

A) None of my pets can flap their wings. 
B) No birds can flap their wings. 
C) All my pets can flap their wings. 
D) All birds can flap their wings. 
A) None of my pets can flap their wings. 
B) No birds can flap their wings. 
C) All my pets can flap their wings. 
D) All birds can flap their wings.

Question 17

Solve the problem.
-Given that $\mathrm { p } \vee \mathrm { q }$ is false, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

Accepted Answer

A)  At least one of $p$ and $q$ is false 
B)  Exactly one of $p$ and $q$ is false 
C)  $p$ and $q$ have the same truth value 
D)  Both $p$ and $q$ are false 
A)  At least one of $p$ and $q$ is false 
B)  Exactly one of $p$ and $q$ is false 
C)  $p$ and $q$ have the same truth value 
D)  Both $p$ and $q$ are false

Question 18

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

Accepted Answer

A) 
  
B)  
  
C) 
  
D) 
  
A) 
  
B)  
  
C) 
  
D)

Question 19

Write a negation for the statement.
-Not all people like football.

Accepted Answer

A) Some people like football. 
B) Some people do not like football. 
C) All people do not like football. 
D) All people like football. 
A) Some people like football. 
B) Some people do not like football. 
C) All people do not like football. 
D) All people like football.

Question 20

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

Accepted Answer

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

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

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

When using a truth table, the statement $\sim \mathrm { p } \vee \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \wedge \mathrm { q } )$ .

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

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

The argument has a true conclusion. Identify the argument as valid or invalid. -Eric is older than Camille. $\underline { \text {Camille is older than Todd.} }$ Todd is younger than Eric.

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

Decide whether the statement is true or false. - $\text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. }$

Construct a truth table for the statement. - $\sim(s \vee t) \wedge \sim(t \wedge s)$

Determine whether the argument is valid or invalid. -The Rams will be in the playoffs if and only if Ozzie is an all-star. Mark loves the Rams or Ozzie is an all-star. Mark does not love the Rams. Therefore, the Rams will not be in the playoffs.

$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } p \rightarrow q \text {. }$

$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } \sim p \rightarrow q \text {. }$

Write a negation of the inequality. Do not use a slash symbol. - $x < 5$

Decide whether the statement is true or false. - $\text { For no real number } \mathrm { y } , \mathrm { y } < 10 \text { and } \mathrm { y } > 12 \text {. }$

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

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -All birds have wings. None of my pets are birds. All animals with wings can flap them.

Solve the problem. -Given that $\mathrm { p } \vee \mathrm { q }$ is false, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

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

Write a negation for the statement. -Not all people like football.

Use a truth table to determine whether the argument is valid. - \rightarrow

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

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

When using a truth table, the statement ∼p∨∼q\sim \mathrm { p } \vee \sim \mathrm { q }∼p∨∼q is equivalent to ∼(p∧q)\sim ( \mathrm { p } \wedge \mathrm { q } )∼(p∧q) .

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

The argument has a true conclusion. Identify the argument as valid or invalid. -Eric is older than Camille. Camille is older than Todd.‾\underline { \text {Camille is older than Todd.} }Camille is older than Todd.​ Todd is younger than Eric.

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

Decide whether the statement is true or false. - For every real number p,p2 is positive and p<p2. \text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. } For every real number p,p2 is positive and p<p2.

Construct a truth table for the statement. - ∼(s∨t)∧∼(t∧s)\sim(s \vee t) \wedge \sim(t \wedge s)∼(s∨t)∧∼(t∧s)

Determine whether the argument is valid or invalid. -The Rams will be in the playoffs if and only if Ozzie is an all-star. Mark loves the Rams or Ozzie is an all-star. Mark does not love the Rams. Therefore, the Rams will not be in the playoffs.

When using a truth table, the statement q→p is equivalent to p→q. \text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } p \rightarrow q \text {. } When using a truth table, the statement q→p is equivalent to p→q.

When using a truth table, the statement q→p is equivalent to ∼p→q. \text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } \sim p \rightarrow q \text {. } When using a truth table, the statement q→p is equivalent to ∼p→q.

Write a negation of the inequality. Do not use a slash symbol. - x<5x < 5x<5

Decide whether the statement is true or false. - For no real number y,y<10 and y>12. \text { For no real number } \mathrm { y } , \mathrm { y } < 10 \text { and } \mathrm { y } > 12 \text {. } For no real number y,y<10 and y>12.

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

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -All birds have wings. None of my pets are birds. All animals with wings can flap them.

Solve the problem. -Given that p∨q\mathrm { p } \vee \mathrm { q }p∨q is false, what can you conclude about the truth values of p\mathrm { p }p and q\mathrm { q }q ?

Construct a truth table for the statement. - p∨(p∧∼p)p \vee ( p \wedge \sim p )p∨(p∧∼p)

Write a negation for the statement. -Not all people like football.

Use a truth table to determine whether the argument is valid. - \rightarrow

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

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

When using a truth table, the statement $\sim \mathrm { p } \vee \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \wedge \mathrm { q } )$ .

The argument has a true conclusion. Identify the argument as valid or invalid. -Eric is older than Camille. $\underline { \text {Camille is older than Todd.} }$ Todd is younger than Eric.

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

Decide whether the statement is true or false. - $\text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. }$

Construct a truth table for the statement. - $\sim(s \vee t) \wedge \sim(t \wedge s)$

$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } p \rightarrow q \text {. }$

$\text { When using a truth table, the statement } q \rightarrow p \text { is equivalent to } \sim p \rightarrow q \text {. }$

Write a negation of the inequality. Do not use a slash symbol. - $x < 5$

Decide whether the statement is true or false. - $\text { For no real number } \mathrm { y } , \mathrm { y } < 10 \text { and } \mathrm { y } > 12 \text {. }$

Solve the problem. -Given that $\mathrm { p } \vee \mathrm { q }$ is false, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

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