Download Exercises for Chapter 2

Describe the elements of the given set using
word description and set-builder notation:
1. A = {Mercury, Venus, Earth, Mars, Jupiter,
Saturn, Uranus, Neptune, Pluto}
2. B = {0, 2, 4, 6, …, 50}
3. C = {1992, 1996, 2000, 2004}
Which pair of sets are equal? equivalent?
1. A is the set of even numbers less than 10.
B is the set of odd numbers between 10 and 20.
2. A = {1, 2, 1, 2, 3, 4, 4}
B = {4, 3, 2, 1}
Homework
1. Give one example of each of the following:
a) a set represented by word description
b) a set represented by roster method
c) a set represented by set-builder
notation that has no element
d) a finite set
e) an infinite set
f) two sets that are equal
g) two sets that are equivalent
2. Given: U = {a, b, c, d, e, f, g}
A = {a, b, f, g}
B = {c, d, e}
C = {a, g}
D = {a, b, c, d, e}
a. Which given set is a subset of a) D?, b) A?
b. Write the elements of a) A and b) C.
c. Which given set is equal to A ?
d. Which given set is equivalent to C?
e. Use a Venn diagram to illustrate B  by
placing the elements in the proper region.
f. Use a Venn diagram to illustrate A and
C.
Given: U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 3, 5, 7}
B = {1, 2, 3}
C = {2, 3, 4, 5,6}
I. Find each of the following sets:
1. A  
7. (A  B )
2. B  
8. A   B 
3. B  U
9. (B  C) 
4. C  U
10. B  C
5. A  B
11. A  B  C
6. B  C
13. A  B  C
II. Draw a Venn diagram for 5 – 13.
A
B
C
Among 120 freshmen at a college, 40 take
mathematics, 50 take English, and 15 take
both mathematics and English. Find the
number of freshmen who:
1.
2.
3.
4.
5.
6.
do not take mathematics.
take mathematics or English.
take mathematics, but not English.
take English, but not mathematics.
take exactly one of the two subjects.
take neither mathematics nor English.
In a sample of 60 people, it was found that
25 read Newsweek magazine, 26 read Time,
26 read Fortune, 9 read both Newsweek and
Fortune, 11 read both Newsweek and Time,
8 read both Time and Fortune, and 3 read
all three magazines.
1. Fill in the correct number of people in
each of the eight regions of the Venn
diagram where N, T, and F denote the
set of people who read Newsweek, Time,
and Fortune, respectively.
2. Find the number of people who read a) only
one magazine, b) at least one magazine,
c) exactly two magazines, d) no magazine.