Question

1. Write the set { x | x ∈ R, x2 = 4 or x
2 = 9} in list form.
2. {x: x is a real number between 1 and 2} is an
a) finite set
b) empty set
c) infinite set
3. Write set {1, 5, 15, 25,…} in set-builder form.
4. What is the cardinality of each of these sets?
a) {{a}}
b) {a, {a}}
c) {a, {a}, {a, {a}}}
d) {∅}
e) {∅, {∅}, {∅, {∅}}}
5. Suppose that A is the set of sophomores at your school and B is the set of students in
discrete mathematics at your school. Express the following set in terms of A and B:
"the set of students at your school who either are not sophomores or are not taking discrete
mathematics"
a. A
c ∩ Bc
b. A
c U B
c
c. B-A
d. A-B
6. Let A be the set of students who live within one mile of school and let B be the set of
students who walk to classes. Describe the set B-A.
a. The set of students who walk to classes but live more than 1 mile away from school.
b. The set of students who walk to classes but live within 1 mile away from school.
c. The set of students who walk to classes.
7. What is the power set of the set {1, a, b}?
8. Let S = {∅, ?,{?}}Determine whether each of these is an element of S, a subset of S, neither,
or both.
a) {?}
b) {{?}}
c) ∅
d) { {∅ }, ?}}
8. Determine whether each of these statements is true or false.
a) 0 ∈ ∅
b) ∅ ∈ {0}
c) {0} ⊂ ∅
d) ∅ ⊂ {0}
e) {0} ∈ {0}
f) {0} ⊂ {0}
g) {∅} ⊆ {∅}
9. Let A = {a, b, c}, B = {x, y}, and C = {0, 1}.
Find A × B × C.
10. Find A2
if A = {0, a, 3}.

Answer 1

Answers :
1. I am a little confused how the question is written if it is then the set will contain 2 and -2 and for
It will be 3 and -3.

2. The answer is C Infinite Set

3. The set builder form will be
{x: either x=1 or x=5n, where n is an odd natural number}

4. Cardinality for
a. {{a}} - 1
b. {a, {a}} - 2
c. {a, {a}, {a, {a}}} - 3
d. {∅} - 1 ( set contain empty set which is a single element)
e. {∅, {∅}, {∅, {∅}}} - 3

5. We can write the description "the set of students at your school who either are not sophomores or are not taking discrete mathematics" in term of A and B as :
  
or using De Morgan's Law we can write is as - .

6. The power set of  {1, a, b} is =  {null, {1} , {a}, {b}, {1,a}, {1,b}, {a,b}, {1,a,b}}.

7. a. {?} is the subset and element of set
b. {{?}} is subset of given set
c.  ∅ - is subset and element of set
d. { {∅ }, ?}} is the subset of set

8.  a. FALSE - the empty set does not contain any element not even 0.
b. FALSE - The set only containing 0 does not contain empty set.
c. FALSE - The only set of empty set is empty set itself
d. True - Empty set is the subset of every set
e. FALSE - The set only containing 0 does not contain any set
f. True - A set is always an inclusive subset of itself.

9. A x B x C = {}

10. if A = {0, a, 3}. then means A x A so
A x A = { (0, 0), (0, a), (0,3), (a,0), (a,a), (a, 3), (3,0), (3,a), (3,3) }

Thank you!!