Question 1

Restate in a logically equivalent form.
-The flowers are not blooming or it is not winter.

Accepted Answer

A) It is not true that the flowers are blooming and it is winter. 
B) The flowers are blooming and it is winter. 
C) It is not true that both the flowers are blooming and it is winter. 
D) It is not true that it is winter and the flowers are not blooming. 
A) It is not true that the flowers are blooming and it is winter. 
B) The flowers are blooming and it is winter. 
C) It is not true that both the flowers are blooming and it is winter. 
D) It is not true that it is winter and the flowers are not blooming. C

Question 2

$$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$$
-$\varnothing _ { - } \varnothing$

Accepted Answer

A)  $\notin$ 
B)  $\in$ 
A)  $\notin$ 
B)  $\in$ A

Question 3

Write the set as indicated.
-Write the odd natural numbers less than 39 using set-builder notation.

Accepted Answer

A)  $\{ x \in N \mid x \leq 39$ and $x$ is odd $\}$ 
B)  $\{ x \in N \mid x \leq 37$ and $x$ is odd $\}$ 
C)  $\{ x \in N \mid x < 38 \}$ 
D)  $\{ x \in N k < 39 \}$ 
A)  $\{ x \in N \mid x \leq 39$ and $x$ is odd $\}$ 
B)  $\{ x \in N \mid x \leq 37$ and $x$ is odd $\}$ 
C)  $\{ x \in N \mid x < 38 \}$ 
D)  $\{ x \in N k < 39 \}$ B

Question 4

Write the set as indicated.
-Write $\{ 2,4,6,8 \}$ using set-builder notation.

Accepted Answer

A)  $\{ x \mid x$ is any even natural number $\}$ 
B)  $\{ 2,4,6,8 \}$ 
C)  $\{ x \mid x$ is any natural number $\}$ 
D)  $\{ x \mid x$ is an even natural number less than $10 \}$ 
A)  $\{ x \mid x$ is any even natural number $\}$ 
B)  $\{ 2,4,6,8 \}$ 
C)  $\{ x \mid x$ is any natural number $\}$ 
D)  $\{ x \mid x$ is an even natural number less than $10 \}$

Question 5

Provide an appropriate response.
-Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. The store is not open today.

Accepted Answer

Today is S

Question 6

Determine the validity of the argument.
-Football and studying don't mix. Don is a football player.
Therefore Don does not study.

Accepted Answer

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

Question 7

Write in if-then form.
-I will lose weight if I diet.

Accepted Answer

A) If I diet, then I gain weight. 
B) If I lose weight, then I'll diet. 
C) If I diet, then I'll lose weight. 
D) If I don't diet, then I won't lose weight. 
A) If I diet, then I gain weight. 
B) If I lose weight, then I'll diet. 
C) If I diet, then I'll lose weight. 
D) If I don't diet, then I won't lose weight.

Question 8

Write the statement indicated.
-State the contrapositive of the following: If he is happy, then he is smiling.

Accepted Answer

A) If he is smiling, then he is happy. 
B) If he is happy, then he is not smiling. 
C) If he is not happy, then he is not smiling. 
D) If he is not smiling, then he is not happy. 
A) If he is smiling, then he is happy. 
B) If he is happy, then he is not smiling. 
C) If he is not happy, then he is not smiling. 
D) If he is not smiling, then he is not happy.

Question 9

Determine the validity of the argument.
-Sailboats need a windy day to sail. Today is a windy day.
Therefore today is a good day for sailing sailboats.

Accepted Answer

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

Question 10

Determine the validity of the argument.
-Some winter days are cold. Today, it is cold.
Therefore it is winter.

Accepted Answer

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

Question 11

Negate the following: The store is sometimes open on Sunday.

Accepted Answer

The store

Question 12

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.
-I'll exercise if I don't eat too much.

Accepted Answer

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

Question 13

Determine the validity of the argument.
-All businessmen wear suits. Aaron wears suits.
Therefore Aaron is a businessman.

Accepted Answer

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

Question 14

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

Accepted Answer

A) 
$\begin{array}{ll}
\mathrm{W} & \mathrm{W} \vee(\mathrm{w} \wedge \sim \mathrm{w}) \
\hline \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{w} \wedge \sim \mathrm{W}) \
\hline \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F}
\end{array}$ 
C) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{W} \wedge \sim \mathrm{W}) \
\hline \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T}
\end{array}$ 
D) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{W} \wedge \sim \mathrm{W}) \
\mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T}
\end{array}$ 
A) 
$\begin{array}{ll}
\mathrm{W} & \mathrm{W} \vee(\mathrm{w} \wedge \sim \mathrm{w}) \
\hline \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{w} \wedge \sim \mathrm{W}) \
\hline \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F}
\end{array}$ 
C) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{W} \wedge \sim \mathrm{W}) \
\hline \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T}
\end{array}$ 
D) 
$\begin{array}{lc}
\mathrm{W} & \mathrm{W} \vee(\mathrm{W} \wedge \sim \mathrm{W}) \
\mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T}
\end{array}$

Question 15

Determine the validity of the argument.
-Not all that glitters is gold. My ring glitters.
Therefore my ring is not gold.

Accepted Answer

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

Question 16

Determine the validity of the argument.
-Some TV shows are comedies. All comedies are hits.
Therefore some TV shows are hits.

Accepted Answer

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

Question 17

Provide an appropriate response.
-Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. Today is Saturday.

Accepted Answer

The store

Question 18

Provide an appropriate response.
-Is the set of multiples of 5 between 1 and 100 well-defined?

Accepted Answer

Yes, you c

Question 19

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
-$2 x + 1 = 5 - x$ (make true)

Accepted Answer

A)  Only two natural numbers $x$ exist such that $2 x + 1 = 5 - x$. 
B)  No natural number $x$ exists such that $2 x + 1 = 5 - x$. 
C)  For every natural number $x , 2 x + 1 = 5 - x$. 
D)  There exists a natural number $x$ such that $2 x + 1 = 5 - x$. 
A)  Only two natural numbers $x$ exist such that $2 x + 1 = 5 - x$. 
B)  No natural number $x$ exists such that $2 x + 1 = 5 - x$. 
C)  For every natural number $x , 2 x + 1 = 5 - x$. 
D)  There exists a natural number $x$ such that $2 x + 1 = 5 - x$.

Question 20

Provide an appropriate response.
-$U$ is the universal set and B is a proper subset of U. Write a relationship between the cardinal numbers of $U , B$ and $\bar { B }$.

Accepted Answer

The answer of Provide an appropriate response.
-$U$ is the universal...

Restate in a logically equivalent form. -The flowers are not blooming or it is not winter.

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $\varnothing _ { - } \varnothing$

Write the set as indicated. -Write the odd natural numbers less than 39 using set-builder notation.

Write the set as indicated. -Write $\{ 2,4,6,8 \}$ using set-builder notation.

Provide an appropriate response. -Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. The store is not open today.

Determine the validity of the argument. -Football and studying don't mix. Don is a football player. Therefore Don does not study.

Write in if-then form. -I will lose weight if I diet.

Write the statement indicated. -State the contrapositive of the following: If he is happy, then he is smiling.

Determine the validity of the argument. -Sailboats need a windy day to sail. Today is a windy day. Therefore today is a good day for sailing sailboats.

Determine the validity of the argument. -Some winter days are cold. Today, it is cold. Therefore it is winter.

Negate the following: The store is sometimes open on Sunday.

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. -I'll exercise if I don't eat too much.

Determine the validity of the argument. -All businessmen wear suits. Aaron wears suits. Therefore Aaron is a businessman.

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

Determine the validity of the argument. -Not all that glitters is gold. My ring glitters. Therefore my ring is not gold.

Determine the validity of the argument. -Some TV shows are comedies. All comedies are hits. Therefore some TV shows are hits.

Provide an appropriate response. -Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. Today is Saturday.

Provide an appropriate response. -Is the set of multiples of 5 between 1 and 100 well-defined?

Use a quantifier to make the following true or false, as indicated, where x is a natural number. - $2 x + 1 = 5 - x$ (make true)

Provide an appropriate response. - $U$ is the universal set and B is a proper subset of U. Write a relationship between the cardinal numbers of $U , B$ and $\bar { B }$ .

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

Restate in a logically equivalent form. -The flowers are not blooming or it is not winter.

Indicate which symbol, ∈ or ∉ makes the statement true. \text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. } Indicate which symbol, ∈ or ∈/ makes the statement true. - ∅−∅\varnothing _ { - } \varnothing∅−​∅

Write the set as indicated. -Write the odd natural numbers less than 39 using set-builder notation.

Write the set as indicated. -Write {2,4,6,8}\{ 2,4,6,8 \}{2,4,6,8} using set-builder notation.

Provide an appropriate response. -Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. The store is not open today.

Determine the validity of the argument. -Football and studying don't mix. Don is a football player. Therefore Don does not study.

Write in if-then form. -I will lose weight if I diet.

Write the statement indicated. -State the contrapositive of the following: If he is happy, then he is smiling.

Determine the validity of the argument. -Sailboats need a windy day to sail. Today is a windy day. Therefore today is a good day for sailing sailboats.

Determine the validity of the argument. -Some winter days are cold. Today, it is cold. Therefore it is winter.

Negate the following: The store is sometimes open on Sunday.

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. -I'll exercise if I don't eat too much.

Determine the validity of the argument. -All businessmen wear suits. Aaron wears suits. Therefore Aaron is a businessman.

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

Determine the validity of the argument. -Not all that glitters is gold. My ring glitters. Therefore my ring is not gold.

Determine the validity of the argument. -Some TV shows are comedies. All comedies are hits. Therefore some TV shows are hits.

Provide an appropriate response. -Write a valid conclusion based on the following statements: The store is open today if and only if it is not Saturday or Sunday. Today is Saturday.

Provide an appropriate response. -Is the set of multiples of 5 between 1 and 100 well-defined?

Use a quantifier to make the following true or false, as indicated, where x is a natural number. - 2x+1=5−x2 x + 1 = 5 - x2x+1=5−x (make true)

Provide an appropriate response. - UUU is the universal set and B is a proper subset of U. Write a relationship between the cardinal numbers of U,BU , BU,B and Bˉ\bar { B }Bˉ .

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

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $\varnothing _ { - } \varnothing$

Write the set as indicated. -Write $\{ 2,4,6,8 \}$ using set-builder notation.

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

Use a quantifier to make the following true or false, as indicated, where x is a natural number. - $2 x + 1 = 5 - x$ (make true)

Provide an appropriate response. - $U$ is the universal set and B is a proper subset of U. Write a relationship between the cardinal numbers of $U , B$ and $\bar { B }$ .