### 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
.

$\{1,5,9,\dots \}$

3
.

$\{c|c\text{is a cat}\}$

4
.

$\{1,2,3,\dots ,1000\}$

5
.

$\{s,m,i,l,e\}$

6
.

$\{m\in \mathbb{N}|m={n}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{where}\phantom{\rule{thinmathspace}{0ex}}n\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{a}\phantom{\rule{thinmathspace}{0ex}}\text{natural}\phantom{\rule{thinmathspace}{0ex}}\text{number}\}$

Use the sets provided to answer the following questions: $U=\{31,32,33,\dots ,50\}$, $A=\{35,38,41,44,47,50\}$, $B=\{32,36,40,44,48\}$, and $C=\{31,32,41,42,48,50\}$.

7
.

Find $A\phantom{\rule{thinmathspace}{0ex}}\text{or}\phantom{\rule{thinmathspace}{0ex}}B$.

8
.

Find $B\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}C$.

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 $(A\cup B{)}^{\prime}\cap C$.

13
.

Find $(A\cap {B}^{\mathrm{\prime}})\cup C$.

Use the Venn diagram below to answer the following questions.

14
.

Find ${B}^{\mathrm{\prime}}$.

15
.

Find $A\cup B$.

16
.

Find $A\cap {B}^{\mathrm{\prime}}$.

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 $n((A\cup B\cup R{h}^{+}{)}^{\mathrm{\prime}})$.

19
.

Find the number of donors who were $\text{A}{}^{+}\phantom{\rule{thinmathspace}{0ex}}\text{or}\phantom{\rule{thinmathspace}{0ex}}\text{B}{}^{+}\phantom{\rule{thinmathspace}{0ex}}\text{or}\phantom{\rule{thinmathspace}{0ex}}\text{AB}{}^{+}$.

20
.

Use Venn diagrams to prove that if $A\subset B$, then $A\cap B=A$.