Contemporary Mathematics

# Chapter Review

### Chapter Review

##### Basic Set Concepts
1 .
A ______________ is a well-defined collection of distinct objects.
2 .
A collection of well-defined objects without any members in it is called the ________ _______.
3 .
Write the set consisting of the last five letters of the English alphabet using the roster method.
4 .
Write the set consisting of the numbers 1 through 20 inclusive using the roster method and an ellipsis.
5 .
Write the set of all zebras that do not have stripes in symbolic form.
6 .
Write the set of negative integers using the roster method and an ellipsis.
7 .
Use set builder notation to write the set of all even integers.
8 .
Write the set of all letters in the word Mississippi and label it with a capital $M$.
9 .
Determine whether the following collection describes a well-defined set: "A group of these five types of apples: Granny Smith, Red Delicious, McIntosh, Fuji, and Jazz."
10 .
Determine whether the following collection describes a well-defined set: "A group of five large dogs."
11 .
Determine the cardinality of the set $A = \{ {\text{Alabama}},{\text{ Alaska}},{\text{ Arkansas}},{\text{ Arizona}}\}$.
12 .
Determine whether the following set is a finite set or an infinite set: $F = \{ 5,10,15, \ldots \}$.
13 .
Determine whether sets $A$ and $B$ are equal, equivalent, or neither: $A = \{a,b,c\}$ and $B = \{ 1,2,3,4\}$.
14 .
Determine if sets $A$ and $B$ are equal, equivalent, or neither: $A = \{a, b,c\}$ and $B = \{c,a,b\}$.
15 .
Determine if sets $A$ and $B$ are equal, equivalent, or neither: $A = \{a,b,c\}$ and $B = \{ 1,2,3\}$.
##### Subsets
16 .
If every member of set $A$ is also a member of set $B$, then set $A$ is a _________ of set $B$.
17 .
Determine whether set $A$ is a subset, proper subset, or neither a subset nor proper subset of set $B$: $A = \{s,o,n\}$ and $B = \{s,o,n,g\}$.
18 .
Determine whether set $A$ is a subset, proper subset, or neither a subset nor proper subset of set $B$: $A = \{s,o,n\}$ and $B = \{s,o,l\}$.
19 .
Determine whether set $A$ is a subset, proper subset, or neither a subset nor proper subset of set $B$: $A = \{s,o,n\}$ and $B = \{o,n,s\}$.
20 .
List all the subsets of the set $\{ {\text{up,}}\,{\text{down}}\}$.
21 .
List all the subsets of the set $\{ 0\}$.
22 .
Calculate the total number of subsets of the set {Scooby, Velma, Daphne, Shaggy, Fred}.
23 .
Calculate the total number of subsets of the set {top hat, thimble, iron, shoe, battleship, cannon}.
24 .
Find a subset of the set $\{g,r,e,a,t\}$ that is equivalent, but not equal, to $\{t,e,a\}$.
25 .
Find a subset of the set $\{g,r,e,a,t\}$ that is equal to $\{t,e,a\}$.
26 .
Find two equivalent finite subsets of the set of natural numbers, $\mathbb{N} = \{ 1,2,3, \ldots \}$, with a cardinality of 4.
27 .
Find two equal finite subsets of the set of natural numbers, $\mathbb{N} = \{ 1,2,3, \ldots \}$, with a cardinality of 3.
##### Understanding Venn Diagrams
28 .
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
29 .
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words:
30 .
Draw a Venn diagram to represent the relationship between the described sets: Falcons $\subset$ Raptors.
31 .
Draw a Venn diagram to represent the relationship between the described sets: Natural numbers $\subset$ Integers $\subset$ Real numbers.
32 .
The universal set is the set $U = \{s,m,i,l,e\}$. Find the complement of the set $E = \{e,l,m\}$.
33 .
The universal set is the set $U = \{ 1,2,3, \ldots \}$. Find the complement of the set $V = \{ 18,19,20, \ldots \}$.
34 .
Use the Venn diagram below to determine the members of the set ${A^\prime }$.
35 .
Use the Venn diagram below to determine the members of the set ${A^\prime }$.
##### Set Operations with Two Sets
Determine the union and intersection of the sets indicated: $U = \{ a,b,c, \ldots ,z\}$, $S = \{s,c,r,a,b,l,e\}$, $B = \{b,r,a,c,e\}$, $C = \{c,r,a,b\}$, $R = \{r,i,s,k\}$, and $Q = \{q,u,i,z\}$.
36 .
What is $S \cap R$?
37 .
What is $S \cup B$?
38 .
Write the set containing the elements in sets $B\,{\text{or}}\,Q$.
39 .
Write the set containing all the elements is both sets $B\,{\text{and}}\,Q$.
40 .
Find $C\,{\text{intersection}}\,R$.
41 .
Find $C\,{\text{union}}\,R$.
42 .
Find the cardinality of $C \cup R,\,n(C \cup R)$.
43 .
Find $n(S\,{\text{union}}\,R)$.
44 .
Use the Venn diagram below to find $A \cap B$.
45 .
Use the Venn diagram below to find $n(A \cup B)$.
##### Set Operations with Three Sets
Use the Venn diagram below to answer the following questions.
46 .
Find $n(A \cup C)$.
47 .
Find $n(B \cap C)$.
48 .
A food truck owner surveyed a group of 50 customers about their preferences for hamburger condiments. After tallying the responses, the owner found that 24 customers preferred ketchup, 11 preferred mayonnaise, and 31 preferred mustard. Of these customers, eight preferred ketchup and mayonnaise, one preferred mayonnaise and mustard, and 13 preferred ketchup and mustard. No customer preferred all three. The remaining customers did not select any of these three condiments. Draw a Venn diagram to represent this data.
49 .
Given $U = \{ {\text{r,}}\,{\text{s,}}\,{\text{t,}}\,{\text{l,}}\,{\text{n,}}\,{\text{e,}}\,{\text{i,}}\,{\text{a}}\}$, $R = \{ {\text{r,}}\,{\text{e,}}\,{\text{s,}}\,{\text{t}}\}$, $S = \{ {\text{s,}}\,{\text{t,}}\,{\text{a,}}\,{\text{i,}}\,{\text{r}}\}$, and $L = \{ {\text{l,}}\,{\text{i,}}\,{\text{n,}}\,{\text{e,}}\,{\text{s}}\}$, find $(S \cup R) \cap {L^\prime }$.
50 .
Use Venn diagrams to prove that if $A \subset B$, then ${B^\prime } \subset {A^\prime }$.
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