Name ________________________________________
Date __________ Period _______
ws 1 - Set Theory Notation & Introduction
1.
Notation & Vocabulary:
a. What is the correct notation for “is
M”?
an element of”?
______________________________
______________________________
j. What is the correct notation for a set?
b. What is the correct notation for
______________________________
“union”?
k. What does
______________________________
Æ mean?
______________________________
c. What is the correct notation for
l. What does
“intersection”?
Q mean?
______________________________
______________________________
m. What do Braces denote?
d. What is the correct notation for the
______________________________
Universal Set?
n. What does
______________________________
U mean?
______________________________
e. What is the correct notation for “is a
o. What does
subset of”?
Ì mean?
______________________________
______________________________
p. What does
f. What is the correct notation for “is a
mean?
______________________________
proper subset of”?
q. What does | mean?
______________________________
______________________________
g. What is the correct notation for “such
r. What does
that”?
Î mean?
______________________________
______________________________
s. What does
h. What is the correct notation for the
mean?
______________________________
Null Set, or the Empty Set?
t. What does
______________________________
mean?
______________________________
i. What are at least two correct
notations for “the complement of set
Write the following sets in roster form:
2.
The set of integers between -2 and 2. ______________________________________________
3.
The set of letters in the word LOYAL. ______________________________________________
4.
The set of letters in the word CHOICE. _____________________________________________
5.
The set of all factors of 36. _____________________________________________________
Page 1
Name ________________________________________
Date __________ Period _______
6.
𝑌 = {𝑥|𝑥 𝑖𝑠 𝑎 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑐𝑢𝑏𝑒, 27 < 𝑥 < 216} _______________________________________
7.
𝑀 = {𝑥|𝑥 ∈ 𝑁, 𝑥 2 < 40} _______________________________________________________
8.
𝑉 = {𝑥|𝑥 ∈ 𝑁, 𝑥 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 18} ______________________________________________
9.
𝑇 = {𝑥|𝑥 ∈ 𝑍, 𝑥 > −2} _______________________________________________________
10.
𝑆 = {𝑥|𝑥 ∈ 𝑍, 𝑥 + 1 = 1} _____________________________________________________
Write in set-builder notation:
11.
𝐶 = {𝑃, 𝑅, 𝐼, 𝑁, 𝐶, 𝐴, 𝐿}
_________________________________________________________________________
12.
𝐻 = {𝐽𝑎𝑛𝑢𝑎𝑟𝑦, 𝐽𝑢𝑛𝑒, 𝐽𝑢𝑙𝑦}
_____________________________________________________________________
13.
𝐼 = {𝑎, 𝑒, 𝑖, 𝑜, 𝑢}
______________________________________________________________________________
14.
𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔, ℎ, 𝑖, 𝑗, 𝑘, 𝑙, 𝑚, 𝑛, 𝑜, 𝑝,
𝐽={
}
𝑞, 𝑟, 𝑠, 𝑡, 𝑢, 𝑣, 𝑤, 𝑥, 𝑦, 𝑧
_________________________________________________________
15.
𝐾 = {1,3,5,7,9}
______________________________________________________________________________
16.
The set of all b such that b is an element of the Integers and b is less than or equal to
positive thirteen.
________________________________________________________________________________
___________
17.
The set of all b such that b is an element of the natural numbers and b is less than or equal
to positive fifteen.
________________________________________________________________________________
___________
Write a description of the set:
Page 2
Name ________________________________________
Date __________ Period _______
18.
{x | x Î W, x ¹ -3}
_________________________________________________________________________
________________________________________________________________________________
____________
19.
{x | x Î R, x > 0}
___________________________________________________________________________
________________________________________________________________________________
____________
20.
{𝑥|𝑥 ∈ 𝑅, 𝑥 ≤ 18}
_____________________________________________________________________________
________________________________________________________________________________
____________
Determine if the following statements are true or false. If the statement is false, state why.
21.
1  {1,2,3}
T/F
30.

22.
2  {1,2,3}
T/F
31.
1  {1,2,3}
T/F
23.
0  {1,2,3}
T/F
32.
{1}  {1,2,3}
T/F
24.
  {1,2,3}
T/F
33.
{1}  {{1,2,3}}
T/F
25.
{1}  {1,2,3}
T/F
34.
{1}  {{1},{2}}
T/F
26.
{1}  {{1,2,3}}
35.
  {1,2,3}
27.
{1}  {{1},{2},{3}}
36.
  {{1,2,3}}
28.
1
T/F
37.

29.
0
T/F
T/F
T/F
Given:
𝐴 = {3,5,7,9}
𝐵 = {2,4,6,8,10}
Page 3
T/F
T/F
T/F
T/F
Name ________________________________________
Date __________ Period _______
𝐶 = {12,14,18,20,24}
𝐷 = {21,26,31,36}
True or False:
38.
13 ∈ 𝐶
39.
6∉𝐴
40.
9∉𝐴
41.
24 ∈ 𝐶
42.
31 ∈ 𝐷
T/F
T/F
43.
36 ∉ 𝐷
T/F
T/F
44.
20 ∉ 𝐶
T/F
45.
9∈𝐴
T/F
T/F
T/F
Fill in the Blank with the best choice:
46.
47.
3 ∈ ____
4 ____ B
50.
5 ____ A
51.
{6} ____ C
48.
{26} ____ C
52.
{21} ____ D
49.
8 ∈
53.
18 ____ B
____
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