Question 1

Write the set as indicated.
-List the set of states that border California.

Accepted Answer

A) {Nevada, Utah} 
B) {Washington, Utah, Arizona} 
C) {Oregon, Nevada, Utah} 
D) {Oregon, Nevada, Arizona} 
A) {Nevada, Utah} 
B) {Washington, Utah, Arizona} 
C) {Oregon, Nevada, Utah} 
D) {Oregon, Nevada, Arizona}

Question 2

Write the statement indicated.
-State the contrapositive of the following: If it is pouring, then it is raining.

Accepted Answer

A) If it is not pouring, then it is not raining. 
B) If it is pouring, then it is not raining. 
C) If it is raining, then it is pouring. 
D) If it is not raining, then it is not pouring. 
A) If it is not pouring, then it is not raining. 
B) If it is pouring, then it is not raining. 
C) If it is raining, then it is pouring. 
D) If it is not raining, then it is not pouring.

Question 3

Do the following represent equal sets?
-{28, 30, 32, 34, 36} = {30, 32, 34, 36}

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 4

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
-$12 x = 5 x + 7 x$ (make false)

Accepted Answer

A)  More than one natural number $x$ exists such that $12 x = 5 x + 7 x$. 
B)  For every natural number $x , 12 x = 5 x + 7 x$. 
C)  There exists a natural number $x$ such that $12 x = 5 x + 7 x$. 
D)  There is no natural number $x$ such that $12 x = 5 x + 7 x$. 
A)  More than one natural number $x$ exists such that $12 x = 5 x + 7 x$. 
B)  For every natural number $x , 12 x = 5 x + 7 x$. 
C)  There exists a natural number $x$ such that $12 x = 5 x + 7 x$. 
D)  There is no natural number $x$ such that $12 x = 5 x + 7 x$.

Question 5

Determine whether the statements are logically equivalent.
-$\mathrm { q } \rightarrow \mathrm { p }$ and $\sim \mathrm { p } \rightarrow \sim \mathrm { q }$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 6

Restate in a logically equivalent form.
-If a triangle is equilateral, then its sides are equal.

Accepted Answer

A) If the sides of a triangle are equal, then it is not equilateral. 
B) If a triangle is not equilateral, then its sides are equal. 
C) If the sides of a triangle are not equal, then it is equilateral. 
D) If the sides of a triangle are not equal, then it is not equilateral. 
A) If the sides of a triangle are equal, then it is not equilateral. 
B) If a triangle is not equilateral, then its sides are equal. 
C) If the sides of a triangle are not equal, then it is equilateral. 
D) If the sides of a triangle are not equal, then it is not equilateral.

Question 7

Determine whether the statements are logically equivalent.
-$\sim ( q \rightarrow p )$ and $q \wedge \sim p$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 8

Find n(A)for the set A.
-$$A = \{ 2,2,3,3 , \ldots , 6,6 \}$$

Accepted Answer

A)  $n ( A ) = 3$ 
B)  $n ( A ) = 5$ 
C)  $n ( A ) = 6$ 
D)  $n ( A ) = 10$ 
A)  $n ( A ) = 3$ 
B)  $n ( A ) = 5$ 
C)  $n ( A ) = 6$ 
D)  $n ( A ) = 10$

Question 9

Find n(A)for the set A.
-$A = \{ x \mid x$ is a number on a clock face $\}$

Accepted Answer

A)  $n ( A ) = 6$ 
B)  $n ( A ) = 3$ 
C)  $n ( A ) = 12$ 
D)  $\mathrm { n } ( \mathrm { A } ) = 24$ 
A)  $n ( A ) = 6$ 
B)  $n ( A ) = 3$ 
C)  $n ( A ) = 12$ 
D)  $\mathrm { n } ( \mathrm { A } ) = 24$

Question 10

Determine the validity of the argument.
-Not all cars are considered sporty. Not all cars are safe at high speeds.
Therefore sports cars are safe at high speeds.

Accepted Answer

A) Not valid 
B) Valid 
A) Not valid 
B) Valid

Question 11

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

Accepted Answer

A) 
$\begin{array}{cccc}
\mathrm{s} & \mathrm{r} & \mathrm{P} & \mathrm{s} \vee \sim(\mathrm{r} \wedge \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{s} & \mathrm{r} & \mathrm{P} & \mathrm{s} \vee \sim(\mathrm{r} \wedge \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
A) 
$\begin{array}{cccc}
\mathrm{s} & \mathrm{r} & \mathrm{P} & \mathrm{s} \vee \sim(\mathrm{r} \wedge \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{s} & \mathrm{r} & \mathrm{P} & \mathrm{s} \vee \sim(\mathrm{r} \wedge \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$

Question 12

Write the set as indicated.
-List the counting numbers that are multiples of 5.

Accepted Answer

A) {0, 5, 10, 15, . . .} 
B) $ \varnothing$ 
C) {10, 15, 20, . . .} 
D) {5, 10, 15, . . .} 
A) {0, 5, 10, 15, . . .} 
B) $ \varnothing$ 
C) {10, 15, 20, . . .} 
D) {5, 10, 15, . . .}

Question 13

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form.
-If the food is good or if I eat too much, I'll exercise.

Accepted Answer

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

Write the set as indicated. -List the set of states that border California.

Write the statement indicated. -State the contrapositive of the following: If it is pouring, then it is raining.

Do the following represent equal sets? -{28, 30, 32, 34, 36} = {30, 32, 34, 36}

Use a quantifier to make the following true or false, as indicated, where x is a natural number. - $12 x = 5 x + 7 x$ (make false)

Determine whether the statements are logically equivalent. - $\mathrm { q } \rightarrow \mathrm { p }$ and $\sim \mathrm { p } \rightarrow \sim \mathrm { q }$

Restate in a logically equivalent form. -If a triangle is equilateral, then its sides are equal.

Determine whether the statements are logically equivalent. - $\sim ( q \rightarrow p )$ and $q \wedge \sim p$

Find n(A)for the set A. - $A = \{ 2,2,3,3 , \ldots , 6,6 \}$

Find n(A)for the set A. - $A = \{ x \mid x$ is a number on a clock face $\}$

Determine the validity of the argument. -Not all cars are considered sporty. Not all cars are safe at high speeds. Therefore sports cars are safe at high speeds.

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

Write the set as indicated. -List the counting numbers that are multiples of 5.

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -If the food is good or if I eat too much, I'll exercise.

An Introduction to Problem Solving

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 2: Introduction to Logic and Sets