SETS
A SET is a well defined group of objects or symbols. The objects or symbols are called the
ELEMENTS of the set. If an element e belongs to a set S, this is represented as e ∈ S. ( ∉ – not an
element)
Exercise
1. In the following questions
i)
write down another two elements of the set.
a)
{2, 4, 6, 8, ………., ………..}
b)
{Sunday, Monday, Tuesday, ………….……..…., ………….….……..}
c)
{a, e, i, ………., ………..}
d)
{1, 3, 5, 7, 9, ………., ………..}
e)
{1, 4, 9, 16, 25, ………., ………..}
2. List the elements in the following sets.
a) A = {months of the year}
b)
B = {even numbers less than 10}
c)
C = {x: 3 ≤ x < 12}
d)
D = {y: y is prime and y< 10}
SUBSETS
Notations
X ⊆ Y – A subset
X ⊈ Y – Not a Subset
A = ∅ or { } – Empty set
Exercise
1.
J = {p, q, r}
a)
List all the subsets of J.
2. P = {whole numbers less than 30}
a)
List the subset Q {Even numbers}
b)
List the subset R {Odd numbers}
c)
List the subset S {Prime numbers}
d)
List the subset T {Square numbers}
Venn Diagram
Notation.
 – Universal Set – for any particular problem is the set which contains all the possible elements for that
problem).
A’ – Complement – the set of elements which are in  but not in A.
⋃ – Union – all the elements in either or both sets.
∩ – Intersection – the common elements in both sets.
n(A) – number of elements in set A
Venn diagrams are the principal way of showing sets diagrammatically. The method consists primarily of
entering the elements of a set into a circle or circles.
Exercise
1)
Using the Venn diagram, indicate whether the following statements are true or false.
a)
5∈A
b)
A
20 ∈ B
5
15
c)
10
20 ∉ A
30
40
20
50
d)
B
50 ∈ A
e)
A ∩ B = {10, 20}
2)
For each of the Venn diagram identify the set
a)
AUB
A
A∩B
b)
1
n(A)
n(A U B)
d
f
8
B
g
e
For the following Venn diagram identify the set
a)

c) A ∩ B
b) A’
e) (A ∩ B)’
d) A U B

A
5
7
2
B
1
3
4
8
6
4)
e)
b
c
6
3)
a
7
9
16
d)
A
B
5
4
A’
c)
P = {2, 3, 5, 7, 11, 13, 17}
Q = {11, 13, 15, 17, 19}
a)
Draw a Venn diagram to illustrate the above information.
b)
c)
Identify the set i) P ∩ Q
ii) P’ U Q
f) A ∩ B’
h
5)
Draw Venn diagrams to represent the following information.
a)
P = {1, 4, 7, 9, 11, 15}
Q = {5, 10, 15}
R = {1, 4, 9}
b)
X = {a, c, d, e, f, g, l}
Y = {b, c, d, e, h, i, k, l, m}
Z = {c, f, i, j, m}
SHADING VENN DIAGRAM
A U B
A
B
2
3
2, 3
A
3, 4
B
2
3
4
1
4
A ∩ B
2, 3
1
A
3, 4
B
2
3
4
1
A’
A
A’ ∩ B
B
2
3
1, 4
4
A
3, 4
1
B
2
3
4
1
Exercise
Shade the region described.

A
B

A
B

A
B
A’ U B
A’ ∩ B’
(A ∩ B)’

A
B
A
B
A
B


A’ U B’
(A U B)’
(A’ ∩ B)’
WORD PROBLEMS/ PAST PAPER QUESTION
1. Twenty boys in a form all play either football or basketball (or both). If thirteen play football and ten
play basketball, how many play both sports?
2. Of the 53 staff at a school, 36 drink tea, 18 drink coffee and 10 drink neither tea nor coffee. How
many drink both tea and coffee?
3. Of the 32 pupils in a class, 18 plays golf, 16 plays the piano and 7 play both. How many play
neither?
4. The sets M and N intersects such that n(M) = 31, n(N) = 18 and n(M U N) = 35. How many
elements are in both M and N?
5. The sets P and Q intersects such that n(P) = 11, n(Q) = 29 and n(P U Q) = 37. How many elements
are in both P and Q?
8.
(a) In Diagram 1, shade the area which represents AUB’.
(b) Describe in set notation the shaded area in Diagram 2.