3.1/
15, 10, 22, 23, 37, 41, 50
1. Let
S
= {2, 5, 17, 27}.
Which of the following are true?
a. 5
œ
S
b. 2 +5
œ
S
c. {}
œ
S
d.
S
œ
S
Note that 2 + 5 = 7, which is not in
S
.
There are no sets that are elements of
S
, so {} and
S
can't be in
S
2. Let
B
= {
x  x
œ
and 1 <
x
< 2}.
Which of the following are true?
a. 0
œ
B
b. 1
œ
B
c. 0.84
œ
B
d.
◊
2
œ
B
Note that 1 is not less than 1, and that
◊
2 is not in
3. How many different sets are described in the following?
What are they?
{2, 3, 4}
set
A
{
}
set
B
{
x  x
is the first letter of cat, bat or apple}
set
C
{
x  x
is the first letter of cat, bat and apple}
set
B
{
x  x
œ
N
and 2 <=
x
<= 4}
set
D
{2,
a
, 3,
b
, 4,
c
}
set
E
{a, b, e}
set
F
{3, 4, 2}
set
D
Note that since no letter can be the first letter of cat, bat and apple, that set is empty.
4. Describe each of the following sets by listing its elements:
a. {
x  x
œ
and
x
2
< 25}
{0, 1, 2, 3, 4}
b. {
x  x
œ
and
x
is even and 2 <
x
< 11}
{4, 6, 8, 10}
c. {
x  x
is one of the first three presidents of the United States}
{Washington, Adams, Jefferson}
d. {
x  x
œ
and
x
2
= 1}
e. {
x  x
is one of the New England states}
{Maine, Vermont, New Hampshire, Massachusetts, Rhode Island, Connecticut}
f. {
x  x
œ
and 
x
 < 4}
{3, 2, 1, 0, 1, 2, 3}
5. Describe each of the following sets by listing its elements:
a. {
x  x
œ
and
x
2
– 5
x
+ 6 = 0}
{2, 3}
b. {
x  x
œ
and
x
2
= 7}
{}
c. {
x  x
œ
and
x
2
 2
x 
8 = 0}
{4}
(note that 2 is not in
)
10. Let
A
= {
x  x
œ
and 1 <
x
< 50},
B
= {
x  x
œ
and 1 <
x
< 50},
C
= {
x  x
œ
and
x

¥
25}
Which of the following statements are true?
a.
A
Œ
B
b. 17
œ
A
c.
A
Œ
C
5 is in
A
, but not in
C
d. 40
œ
C
e.
◊
3
œ
B
f. {0, 1, 2}
Œ
A
0 is not in
A
g. {}
œ
B
I don't see any empty sets listed as an element of
B
, do you?
h.{
x  x
œ
Z and
x
2
¥
625}
Œ
C
22. Find
P
(S) for
S
= {1, 2, 3, 4}.
How many elements do you expect to have?
We would expect 2
4
subsets.
They are: {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, .
.. ,
{1, 2, 3, 4}.
23. Find
P
(S) for
S
= {
f
}.
P
({
f
}) = {{}, {
f
}}
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document37.
Let
A
= {
p, q, r, s
},
B
= {
r, t, v
} and
C
= {
p, s, t, u
} be subsets of
S
= {
p, q, r, s, t, u, v, w
}.
Find
a.
B
…
C
{
t
}
b.
A
»
C
{
p, q, r, s, t, u
}
c.
C
'
{
q, r, v, w
}
d.
A
…
B
…
C
{}
e.
B – C
{
r, v
}
f. (
A
»
B
)'
{
u, w
}
g.
A
µ
B
{(
p,r
), (
p,t
), (
p,v
), (
q,r
), (
q,t
), (
q,v
), (
r,r
), (
r,t
), (
r,v
), (
s,r
), (
s,t
), (
s,v
)}
h. (
A
»
B
)
…
C
'
{
q, r, v
}
41.
Let
A =
{
x

x
is a word that appears before
dog
in an English Dictionary}
B
=
{
x

x
is a word that appears after
canary
in an English Dictionary}
C
=
{
x

x
is a word of more than four letters}
Which of the following are true statements?
a.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 landis
 Sets, Probability, Numerical digit, binary strings, standard 52card deck, freshen breath

Click to edit the document details