Algebraic Connections
Chapter 2 Review
Name:
1. Express the following set as a word description:
a. A = {1, 2, 3, 4, 5}
Set A is the set of numbers between 0 and 6.
b. B = {x | x is one of the first five letters of the alphabet}
Set B is the set of the first five letters of the alphabet.
2. Express the following set in Roster Method:
a. Set B is the set of days of the week that start with T.
B = {Tuesday, Thursday}
b. C = {x│x is one of the last 5 letters of the alphabet}
C = {v, w, x, y, z}
3. Express the following sets in Set Notation:
a. C = {2, 4, 6, 8, 10}
C = {x│x is a multiple of 2 between 1 and 11}
b. Set S is a day of the week ending in y.
S = {x│x is a day of the week ending in y}
4. Find the cardinal number for the following set: G = {1, 2, 3, …, 10}
10
5. Determine whether each of the following statement is true or false. If the statement is false, explain
why.
a. 93  {1, 2, 3, 4, …, 100}? True
b. {d}  {a, b, c, d, e}? False {d} is NOT an element of the set, d would be an element of the set.
c.
The cardinal number for the set {Monday, Tuesday, Wednesday} is 1?
False – the cardinal # is 3.
d. If set A = {1, 2, 3} and set B = {4, 5, 6 }, then set A is equivalent to Set B?
True
e. If set C = {0, 2, 4, 6, 8} and set D = {2, 0, 4, 6}, then set C is equal to set D?
False – to be equal, sets must be EXACTLY alike.
f. 25  {x|x is a multiple of 10}?
True
g. {3, 2, 1}  {1, 2, 3}?
True
h. {1, 2, 3}  {3, 1, 2}?
False – the sets have the same number of elements (cannot be proper subsets0
i. {1, 2, 3}  {1, 2, 3, 4}?
True
j. {1, 2}  { }? False – { } is a subset of {1, 2}, but not the other way around
k. {a, b, c} has 8 subsets?
True
l. {a, b, c, d, e} has 32 proper subsets?
6. Set X = {Alabama, Tennessee}.
a. How many subsets exist for this set?
b. How many proper subsets exist?
False – this set has 31 proper subsets.
2n = 22 = 4
2n - 1= 22 - 1= 4 – 1 = 3
c. List all subsets.
{ }, {AL}, {TN}, {AL, TN}
7. Use the information below to answer the following questions.
U = {1, 2, 3, 4, 5}
A = {1, 2, 3}
B = {2, 3}
C = {1, 3, 5}
a. A’ = {4, 5}
b. A  B = {1, 2, 3}
c. A  B = {2, 3}
d. A  Ø = { }
e. A  Ø = {1, 2, 3}
f. (A  B)’ = {4, 5}
8. Use the information below to answer the following questions.
U = {1, 2, 3, 4, 5, 6}
A = {2, 4, 6}
B = {1, 3, 5, 6}
C = {2, 3, 4}
a. A  B  C = {1, 2, 3, 4, 5, 6}
b. A’  (B  C) = {1, 3, 5}
c. A  B  C = { }
9. Use the diagram to answer the following questions.
U
A
B
II
I
III
IV
V
V
VI
VII
C
a. Which regions represent set A? I, II, IV, V
b. Which regions represent set A’? III, VI, VII, VIII
c. Which regions represent A  B? I, II, III, IV, V, VI
d. Which regions represent A  B  C? V
e. Which regions represent regions A’  C? VI, VII
VIII
10. If set A contains 20 elements, set B contains 30 elements, and the two sets have 10 elements in common,
how many elements are in A  B?
20 + 30 – 10 = 40
11. Set A contains 20 elements, B contains 15 elements, and they have 5 elements in common. Find A  B.
20 + 15 – 5 = 30
12. A survey was taken to determine the sport that received the biggest following. Students were asked
which sports there were interested in. The results were as follows:
Basketball
27 students liked baseball
Baseball
47 students liked football
35 students liked basketball
5
5
6
24 students liked football and basketball
17 students liked football and baseball
10
15 students liked basketball and baseball
7
14
10 students liked basketball, baseball, and football
If 75 students were surveyed,
a. How many students only liked football? 16
16
12
b. How many students only liked basketball? 6
Football
c. How many students liked football or baseball? 57
d. How many students liked baseball and basketball? 15
e. How many students liked football, but not basketball? 23
f. How many student didn’t like any of these sports? 12