Reading Quiz Section 4.1
1. Which of the following describe the set {0, 1, 2, 3, 4}? Select all that apply.
(a)
x ∈ N
0
: x ≤ 4
(b)
x ∈ Q : x ∈ [0, 4]
(c)
x ∈ Z : x ∈ [0, 4)
(d)
x ∈ Z : x ∈ [0, 4]
2. What is the cardinality of the set
cat, {1, 2}, 2
?
(a) 2
(b) 3
(c) 4
(d) It is an infinite set
3. True or False: An open interval contains its endpoints.
4. True or False: {1, 2, 3} = {3, 1, 2}.
5. Which of the following sets are empty?
(a)
x ∈ R : x
2
< 0
(b)
x ∈ R : x
2
≤ 0
(c)
x ∈ N : x ∈ [0.5, 0.75)
(d) [1, 1]
6. True or False: Every set has a proper subset.
7. True or False: {R} ⊆
{R}
.
8. How many subsets has the set A = {0, 1}?
(a) 1
(b) 2
(c) 3
(d) 4
9. A = B if and only if
(a) A ⊆ B
(b) A ⊆ B and if x /∈ A, then x /∈ B.
(c) B ⊆ A
(d) A ⊊ B and B is finite.
10. Explain why
|
A
|
≤
|
B
|
=⇒ A ⊆ B.
Practice Problems Section 4.1
1. Write each of the following sets in roster notation (i.e. list their elements).
(a)
x ∈ R : x
2
− 5x + 4 = −2
(b)
x ∈ Q : 2x ∈ Z
(c)
n
2
− 1 ∈ Z : n ∈ {−3, −1, 1, 3}
(d)
x ∈ 2Z + 1 : x ∈ (0, 10]
Video Solution
2. Write each of the following sets in set-builder notation.
(a)
. . . , −8, −3, 2, 7, 12, 17, . . .
(b)
2, 3, 5, 7, 11, 13
(c)
1,
1
4
,
1
16
,
1
64
, . . .
Video Solution
3. Let A =
n
0,
0
,
1, 2
,
0, {1, 3}
o
.
Answer each of the following true or false:
(a) 0 ∈ A
(b) {0} ∈ A
(c) 1 ∈ A
(d) {1} ∈ A
(e) {1, 3} ∈ A
(f)
0, {1, 3}
∈ A
What is the cardinality of A?
Video Solution
4. Continuing the previous question, answer true or false:
(a) ∅ ⊊ A
(b) {0} ⊆ A
(c)
{0}
⊆ A
(d) {1, 2} ⊆ A
(e)
{1, 2}
⊆ A
(f)
0, {0}, {1, 3}
⊆ A
(g) A ⊊ A
Video Solution
5. Suppose A ⊆ B ⊆ C and A = C. Show that A = B and B = C .
Video Solution
