Question 1

Write a statement that represents the relationship between the following.
-$A = \{ x \mid 2 < x < 6 , x \in N \}$ and 2

Accepted Answer

A)  $2 = \mathrm { A }$ 
B)  $2 \in \mathrm { A }$ 
C)  $2 \subset \mathrm { A }$ 
D)  $2 \notin \mathrm { A }$ 
A)  $2 = \mathrm { A }$ 
B)  $2 \in \mathrm { A }$ 
C)  $2 \subset \mathrm { A }$ 
D)  $2 \notin \mathrm { A }$

Question 2

Write a valid conclusion based on the statements.
-It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Accepted Answer

A) The squirrels are scurrying. 
B) Squirrels do not scurry during the day. 
C) The squirrels are not scurrying. 
D) Squirrels do not scurry at night. 
A) The squirrels are scurrying. 
B) Squirrels do not scurry during the day. 
C) The squirrels are not scurrying. 
D) Squirrels do not scurry at night.

Question 3

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
-x + y = x - y, where y = 0

Accepted Answer

A) Not a statement 
B) True statement 
C) False statement 
A) Not a statement 
B) True statement 
C) False statement

Question 4

Provide an appropriate response.
-A is the set of all the letters of the alphabet and B is the set of vowels. What kind of relationship exists between the two sets? Also, if C is the set of consonants what is the relationship between B and C?

Accepted Answer

The answer of Provide an appropriate response.
-A is the set...

Question 5

$$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$$
-$0 _{-} \varnothing$

Accepted Answer

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

Question 6

Write a statement that represents the relationship between the following.
-$\mathrm { M } = \varnothing$ and $\mathrm { N } = \{ \}$

Accepted Answer

A)  $\mathrm { M } \subset \mathrm { N }$ 
B)  $M = N$ 
C)  $N \in M$ 
D)  $\mathrm { M } \neq \mathrm { N }$ 
A)  $\mathrm { M } \subset \mathrm { N }$ 
B)  $M = N$ 
C)  $N \in M$ 
D)  $\mathrm { M } \neq \mathrm { N }$

Question 7

Provide an appropriate response.
-Write a valid conclusion based on the following statements: The mall is closed if and only if it is Sunday. The mall is closed.

Accepted Answer

It is Sunday. (The m

Question 8

Rewrite the statement using mathematical symbols.
-$a$ is an element of $\{ k , a , d , z , t \}$.

Accepted Answer

A)  $a \in \{ k , a , d , z , t \}$ 
B)  $\{ a \} \subseteq \{ k , a , d , z , t \}$ 
C)  a $\subset \{ k , a , d , z , t \}$ 
D)  $\{ a \} \in \{ k , a , d , z , t \}$ 
A)  $a \in \{ k , a , d , z , t \}$ 
B)  $\{ a \} \subseteq \{ k , a , d , z , t \}$ 
C)  a $\subset \{ k , a , d , z , t \}$ 
D)  $\{ a \} \in \{ k , a , d , z , t \}$

Question 9

Rewrite the statement using mathematical symbols.
-The set consisting of the elements $k$ and $y$ is a proper subset of $\{ k , b , e , y , u \}$.

Accepted Answer

A)  $\{ \mathrm { k } , \mathrm { y } \} \subseteq \{ \mathrm { k } , \mathrm { b } , \mathrm { e } , \mathrm { y } , \mathrm { u } \}$ 
B)  $\{ \mathrm { k } , \mathrm { y } \} \subset \{ \mathrm { k } , \mathrm { b } , \mathrm { e } , \mathrm { y } , \mathrm { u } \}$ 
C)  $\{ k , y \} \in \{ k , b , e , y , u \}$ 
D)  $\{ k , y \} \sim \{ k , b , e , y , u \}$ 
A)  $\{ \mathrm { k } , \mathrm { y } \} \subseteq \{ \mathrm { k } , \mathrm { b } , \mathrm { e } , \mathrm { y } , \mathrm { u } \}$ 
B)  $\{ \mathrm { k } , \mathrm { y } \} \subset \{ \mathrm { k } , \mathrm { b } , \mathrm { e } , \mathrm { y } , \mathrm { u } \}$ 
C)  $\{ k , y \} \in \{ k , b , e , y , u \}$ 
D)  $\{ k , y \} \sim \{ k , b , e , y , u \}$

Question 10

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.
-The food is good and if I eat too much, then I'll exercise.

Accepted Answer

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

Question 11

Rewrite the statement using mathematical symbols.
-P is the set of even numbers less than 50 and more than 40.

Accepted Answer

A)  $P = \{ 40,42,44,46,48 \}$ 
B)  $Q = \{ 42,44,46,48,50 \}$ 
C)  $P = \{ 42,44,46,48 \}$ 
D)  $\mathrm { Q } = \{ 40,42,44,46,48,50 \}$ 
A)  $P = \{ 40,42,44,46,48 \}$ 
B)  $Q = \{ 42,44,46,48,50 \}$ 
C)  $P = \{ 42,44,46,48 \}$ 
D)  $\mathrm { Q } = \{ 40,42,44,46,48,50 \}$

Question 12

How many one-to-one correspondences are there between two sets with 4 elements each?

Accepted Answer

A) None 
B) 2 
C) 24 
D) 6 
A) None 
B) 2 
C) 24 
D) 6

Question 13

Write the statement indicated.
-State the converse of the following: If you study hard, then your grades will be good.

Accepted Answer

A) If you do not study hard, then your grades will not be good. 
B) If you study hard, then your grades will not be good. 
C) If your grades are good, then you studied hard. 
D) If your grades are not good, then you did not study hard. 
A) If you do not study hard, then your grades will not be good. 
B) If you study hard, then your grades will not be good. 
C) If your grades are good, then you studied hard. 
D) If your grades are not good, then you did not study hard.

Question 14

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

Accepted Answer

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

Question 15

Write the negation of the following: The test is difficult.

Accepted Answer

A) The test is not easy. 
B) The test is very difficult. 
C) The test is not difficult. 
D) The test is not very easy. 
A) The test is not easy. 
B) The test is very difficult. 
C) The test is not difficult. 
D) The test is not very easy.

Question 16

Find n(A)for the set A.
-A = {700, 701, 702, . . ., 7000}

Accepted Answer

A) n(
A) = 6301 
B) n(
A) = 4 
C) n(
A) = 6300 
D) n(
A) = 7000 
A) n(
A) = 6301 
B) n(
A) = 4 
C) n(
A) = 6300 
D) n(
A) = 7000

Question 17

Write the set as indicated.
-List the set of all whole numbers greater than 5 and less than 9.

Accepted Answer

A) {5, 6, 7, 8, 9} 
B) {5, 6, 7, 8} 
C) {6, 7, 8, 9} 
D) {6, 7, 8} 
A) {5, 6, 7, 8, 9} 
B) {5, 6, 7, 8} 
C) {6, 7, 8, 9} 
D) {6, 7, 8}

Question 18

Restate in a logically equivalent form.
-It is not true that both this book is interesting and the book is about stars.

Accepted Answer

A) This book cannot be both interesting and about stars. 
B) Either this book is not interesting or it is not about stars. 
C) This book is both interesting and about stars. 
D) Either this book is interesting or it is about stars. 
A) This book cannot be both interesting and about stars. 
B) Either this book is not interesting or it is not about stars. 
C) This book is both interesting and about stars. 
D) Either this book is interesting or it is about stars.

Question 19

How many one-to-one correspondences are there between the sets $\{ x , y , z , u , v \}$ and $\{ 2,4,6,7,9 \}$ if in each correspondence $x$ must correspond to 7 and $z$ to 6 ?

Accepted Answer

A)  120 
B)  16 
C)  21 
D)  6 
A)  120 
B)  16 
C)  21 
D)  6

Question 20

Write the set as indicated.
-Write $\{ 2 \}$ using set-builder notation.

Accepted Answer

A)  $\{ x \mid x$ is the natural number $2 \}$ 
B)  $\{ x \mid x$ is all natural numbers $\}$ 
C)  $\{ x$ is a constant $\}$ 
D)  $\{ x \}$ 
A)  $\{ x \mid x$ is the natural number $2 \}$ 
B)  $\{ x \mid x$ is all natural numbers $\}$ 
C)  $\{ x$ is a constant $\}$ 
D)  $\{ x \}$

Write a statement that represents the relationship between the following. - $A = \{ x \mid 2 < x < 6 , x \in N \}$ and 2

Write a valid conclusion based on the statements. -It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -x + y = x - y, where y = 0

Provide an appropriate response. -A is the set of all the letters of the alphabet and B is the set of vowels. What kind of relationship exists between the two sets? Also, if C is the set of consonants what is the relationship between B and C?

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $0 _{-} \varnothing$

Write a statement that represents the relationship between the following. - $\mathrm { M } = \varnothing$ and $\mathrm { N } = \{ \}$

Provide an appropriate response. -Write a valid conclusion based on the following statements: The mall is closed if and only if it is Sunday. The mall is closed.

Rewrite the statement using mathematical symbols. - $a$ is an element of $\{ k , a , d , z , t \}$ .

Rewrite the statement using mathematical symbols. -The set consisting of the elements $k$ and $y$ is a proper subset of $\{ k , b , e , y , u \}$ .

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. -The food is good and if I eat too much, then I'll exercise.

Rewrite the statement using mathematical symbols. -P is the set of even numbers less than 50 and more than 40.

How many one-to-one correspondences are there between two sets with 4 elements each?

Write the statement indicated. -State the converse of the following: If you study hard, then your grades will be good.

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

Write the negation of the following: The test is difficult.

Find n(A)for the set A. -A = {700, 701, 702, . . ., 7000}

Write the set as indicated. -List the set of all whole numbers greater than 5 and less than 9.

Restate in a logically equivalent form. -It is not true that both this book is interesting and the book is about stars.

How many one-to-one correspondences are there between the sets $\{ x , y , z , u , v \}$ and $\{ 2,4,6,7,9 \}$ if in each correspondence $x$ must correspond to 7 and $z$ to 6 ?

Write the set as indicated. -Write $\{ 2 \}$ using set-builder notation.

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

Write a statement that represents the relationship between the following. - A={x∣2<x<6,x∈N}A = \{ x \mid 2 < x < 6 , x \in N \}A={x∣2<x<6,x∈N} and 2

Write a valid conclusion based on the statements. -It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -x + y = x - y, where y = 0

Provide an appropriate response. -A is the set of all the letters of the alphabet and B is the set of vowels. What kind of relationship exists between the two sets? Also, if C is the set of consonants what is the relationship between B and C?

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. - 0−∅0 _{-} \varnothing0−​∅

Write a statement that represents the relationship between the following. - M=∅\mathrm { M } = \varnothingM=∅ and N={}\mathrm { N } = \{ \}N={}

Provide an appropriate response. -Write a valid conclusion based on the following statements: The mall is closed if and only if it is Sunday. The mall is closed.

Rewrite the statement using mathematical symbols. - aaa is an element of {k,a,d,z,t}\{ k , a , d , z , t \}{k,a,d,z,t} .

Rewrite the statement using mathematical symbols. -The set consisting of the elements kkk and yyy is a proper subset of {k,b,e,y,u}\{ k , b , e , y , u \}{k,b,e,y,u} .

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. -The food is good and if I eat too much, then I'll exercise.

Rewrite the statement using mathematical symbols. -P is the set of even numbers less than 50 and more than 40.

How many one-to-one correspondences are there between two sets with 4 elements each?

Write the statement indicated. -State the converse of the following: If you study hard, then your grades will be good.

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

Write the negation of the following: The test is difficult.

Find n(A)for the set A. -A = {700, 701, 702, . . ., 7000}

Write the set as indicated. -List the set of all whole numbers greater than 5 and less than 9.

Restate in a logically equivalent form. -It is not true that both this book is interesting and the book is about stars.

How many one-to-one correspondences are there between the sets {x,y,z,u,v}\{ x , y , z , u , v \}{x,y,z,u,v} and {2,4,6,7,9}\{ 2,4,6,7,9 \}{2,4,6,7,9} if in each correspondence xxx must correspond to 7 and zzz to 6 ?

Write the set as indicated. -Write {2}\{ 2 \}{2} using set-builder notation.

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

Write a statement that represents the relationship between the following. - $A = \{ x \mid 2 < x < 6 , x \in N \}$ and 2

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $0 _{-} \varnothing$

Write a statement that represents the relationship between the following. - $\mathrm { M } = \varnothing$ and $\mathrm { N } = \{ \}$

Rewrite the statement using mathematical symbols. - $a$ is an element of $\{ k , a , d , z , t \}$ .

Rewrite the statement using mathematical symbols. -The set consisting of the elements $k$ and $y$ is a proper subset of $\{ k , b , e , y , u \}$ .

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

How many one-to-one correspondences are there between the sets $\{ x , y , z , u , v \}$ and $\{ 2,4,6,7,9 \}$ if in each correspondence $x$ must correspond to 7 and $z$ to 6 ?

Write the set as indicated. -Write $\{ 2 \}$ using set-builder notation.