This document contains a set theory and operations exercise with 15 multiple choice questions. It covers topics like set notation, unions, intersections, subsets, Venn diagrams, and word problems involving sets. The questions test understanding of basic set theory concepts and operations like unions, intersections, complements and subsets. The solutions provide step-by-step workings to arrive at the answers.

1. MATH 1
SET THEORY AND OPERATIONS
Exercises
Write the set notation for the shaded area in each Venn diagram.
B A U B (A U B) ∩ C
(A U B)' (A U B)' ∩ C (A ∩ B) U (A U B)' ∩ C
A ∩ B ∩ C [(A ∩ B ∩ C) U (A U B U C)'] (A U B U C)' U (A ∩ C) U (B ∩ C)
U (B∩ C)

2. MATH 1
SET THEORY AND OPERATIONS
Exercises
Choose the best answer.
1. If A = {11, 13, 15, 17, 19} and B = {12, 13, 15, 17}, what is A U B?
(a) {13, 15, 17}
(b) {11, 12, 19}
(c) {11, 13, 13, 15, 15, 17, 17, 19}
(d) {11, 12, 13, 15, 17, 19}
2. If P = The set of whole numbers less than 5
Q = The set of even numbers greater than 3 but less than 9
R = The set of factors of 6
Then what is (P ∩ Q) U (Q ∩ R)?
(a) {4}
(b) {4, 6}
(c) {4, 6, 8}
(d) {1, 2, 3, 4, 6, 8}
3. Using the same P, Q and R as number 2,
What is (P U Q) ∩ (Q U R)?
(a) {4, 6}
(b) {3, 4, 6}
(c) {2, 3, 4, 6, 8}
(d) {1, 2, 3, 4, 6, 8}
4. From the Venn diagram shown, what is (A ∩ B) U C?
(a) {Mark, Paul, Bart, Matthew}
(b) {Paul}
(c) {Mark, Paul, Matthew}
(d) {Paul, Bart, Matthew}
5. If A is the set of factors of 15,
B is the set of prime numbers less than
C is the set of even numbers less than 9
then what is (A U B) ∩ C?
(a) {1,3,5}
(b) {1,2,3}
(c) {2,3,5}
(d) {2}
6. Which one of the following sets is infinite?
(a) The set of whole numbers less than 10
(b) The set of prime numbers less than 10
(c) The set of integers less than 10
(d) The set of factors of 10
Solution:
a = {1, 2, 3, 4, 5, 6, 7, 8, 9}
b = {1, 3, 5, 7}
c = {….-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

3. d = {1, 2, 5, 10}
Therefore c is infinite
7. A is the set of factors of 12.
Which one of the following is not a member of A?
(a) 3
(b) 4
(c) 5
(d) 6
Solution:
A = {1, 2, 3, 4, 6, 12}
Therefore 5 is not in A.
8. X is the set of multiples of 3
Y is the set of multiples of 6
Z is the set of multiples of 9
Which one of the following is true?
(a) X Y⊂
(b) X Z⊂
(c) Z Y⊂
(d) Z X⊂
Solution:
X = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30...}
Y = {6, 12, 18, 24, 30...}
Z = {9, 18, 27...}
All elements of Z are in X. Therefore Z X.⊂
9. A is the set of factors of 6
B is the set of prime factors of 6
C is the set of proper factors of 6
D is the set of factors of 3
Which of the following is true?
(a) A = B
(b) A = C
(c) B = C
(d) C = D
Solution:
A = the set of factors of 6 = {1, 2, 3, 6}
B = the set of prime factors of 6 = {2, 3}
C = the set of proper factors (proper does not include 1 and the number itself) of 6 = {2, 3}
D = is the set of factors of 3 = {1, 3}
Therefore sets B and C are equal.
10. Which one of the following is the null set?
(a) The set of subsets of the null set
(b) The set of even prime numbers
(c) The set of factors of 7
(d) The set of rational expressions for π
Solution:
The null set is a subset of itself, so the set of subsets of the null set has one element which is the null set itself.
The set of even prime numbers = {2} is not the null set.
The set of multiples of 7 = {1, 7} is not the null set.
π is an irrational number, so cannot be expressed as a rational number.
11. A = {a, b, c, d}

4. How many subsets does the set A have?
(a) 4
(b) 6
(c) 16
(d) 65
Solution:
1 subset with zero elements = ∅
4 subsets with one element = {a}, {b}, {c} and {d}
6 subsets with two elements = {a, b}, {a, c}, {a, d}, {b, c}, {b, d} and {c, d}
4 subsets with three elements = {a, b, c}, {a, b, d}, {a, c, d} and {b, c, d}
1 subset with four elements = {a, b, c, d}
Therefore A has 16 subsets altogether.
Shortcut: If an element has x number of elements, the number of subsets is 2ˣ
or 2 multiplied x times
the set has 4 elements therefore the number of subsets is 2x2x2x2 = 16
12. A, B and C are three sets such that A is a subset of B and B is a subset of C.
Which one of the following statements must always be true?
(a) B is a subset of A
(b) C is a subset of B
(c) C is a subset of A
(d) A is a subset of C
Solution:
A is a subset of B means every element of A is in B
and B is a subset of C means every element of B is in C
Therefore, if both statements are true, it follows that every element of A is in C
13. A is the set of prime numbers less than 10
B is the set of odd numbers less than 10
C is the set of even numbers less than 10
How many of the following statements are true?
A B⊂
B A⊂
A C⊂
C A⊂
B C⊂
C A⊂
(a) 2
(b) 3
(c) 4
(d) none
Solution:
A = {2, 3, 5, 7}
B = {1, 3, 5, 7, 9}
C = {2, 4, 6, 8}
A and B have some members in common. A and C have a member in common. However, no one set is a subset of another.
None of the statements are true.
14. In a group order of milk tea, 5 people wanted pearls in their tea, 12 people wanted jelly in their
tea, and 8 people wanted both pearls and jelly in their tea.
How many people only want jelly in their tea?
(a) 3
(b) 4
(c) 5

5. (d) 8
Solution:
Since the number of people who want jelly includes the the people who want only jelly and the people who want pearls and jelly
jelly = only jelly + pearls and jelly
only jelly = jelly – pearls and jelly
only jelly = 12 – 8
only jelly = 4
15. Sandra asked her 30 classmates whether they had Instagram and Tumblr. She found that:
5 did not have Instagram or Tumblr
7 only have Instagram
15 have both Instagram and Tumblr
How many people only have Tumblr?
(a) 3
(b) 5
(c) 8
(d) 10
Solution:
Number or people who have either Instagram or Tumblr = 30 – 5 = 25
Number of people who have Tumblr = 25 – 7 = 18
Number of people who ONLY have Tumblr = 18 – 15 = 3

6. (d) 8
Solution:
Since the number of people who want jelly includes the the people who want only jelly and the people who want pearls and jelly
jelly = only jelly + pearls and jelly
only jelly = jelly – pearls and jelly
only jelly = 12 – 8
only jelly = 4
15. Sandra asked her 30 classmates whether they had Instagram and Tumblr. She found that:
5 did not have Instagram or Tumblr
7 only have Instagram
15 have both Instagram and Tumblr
How many people only have Tumblr?
(a) 3
(b) 5
(c) 8
(d) 10
Solution:
Number or people who have either Instagram or Tumblr = 30 – 5 = 25
Number of people who have Tumblr = 25 – 7 = 18
Number of people who ONLY have Tumblr = 18 – 15 = 3