Contemporary Mathematics

# Chapter Test

### Chapter Test

1 .
Determine whether the following collection describes a well-defined set: “A group of small tomatoes.”
Classify each of the following sets as either finite or infinite.
2 .
$\{ 1,5,9, \ldots \}$
3 .
$\{ c|c{\text{ is a cat}}\}$
4 .
$\{ 1,2,3, \ldots ,1000\}$
5 .
$\{s,m,i,l,e\}$
6 .
$\{ m \in \mathbb{N}|m = {n^2}\,{\text{where}}\,n\,{\text{is}}\,{\text{a}}\,{\text{natural}}\,{\text{number}}\}$
Use the sets provided to answer the following questions: $U = \{ 31,32,33, \ldots ,50\}$, $A = \{ 35,38,41,44,47,50\}$, $B = \{ 32,36,40,44,48\}$, and $C = \{ 31,32,41,42,48,50\}$.
7 .
Find $A\,{\text{or}}\,B$.
8 .
Find $B\,{\text{and}}\,C$.
9 .
Determine if set $A$ is equivalent to, equal to, or neither equal nor equivalent to set $C$. Justify your answer.
10 .
Find $n(A \cup C)$.
11 .
Find $A \cap (B \cap C)$.
12 .
Find $(A \cup B)' \cap C$.
13 .
Find $(A \cap {B^\prime }) \cup C$.
Use the Venn diagram below to answer the following questions.
14 .
Find ${B^\prime}$.
15 .
Find $A \cup B$.
16 .
Find $A \cap {B^\prime }$.
17 .
Draw a Venn diagram to represent the relationship between the two sets: “All flowers are plants.”
For the following questions, use the Venn diagram showing the blood types of all donors at a recent mobile blood drive.
18 .
Find the number of donors who were $\text{O}{^ - }$; that is, find $n({(A \cup B \cup R{h^ + })^\prime })$.
19 .
Find the number of donors who were $\text{A}{^ + }\,{\text{or}}\,\text{B}{^ + }\,{\text{or}}\,\text{AB}{^ + }$.
20 .
Use Venn diagrams to prove that if $A \subset B$, then $A \cap B = A$.