SECONDARY 2 MATHS
Topic 10 - SETS
A) Defining a Set



A Set is a well-defined collection of items. These items are called the
members or elements of the set.
Capital letters e.g. A, B, C… are used to denote sets.
There are several ways to define a Set :
a) By using words to describe a Set
Ex : E = { pupils who study English}
b) By listing the elements of the Set.
Ex: P = { 2, 3, 5, 7…}
C) By using the Set builder notation
Ex : T = { X : X is an even number between 4 and 9}
B) Set Notation
Set Language
Set Notation
“ …is an element of…”
∈
“….is not an element of ….”
∉
Number of elements in Set A
Universal Set
Empty Set
n (A)
𝜀
∅ or { }
A is subset of B
A ⊆ B
A is a proper subset of B
A⊂B
A is not a subset of B
A⊈B
A is not a proper subset of B
A⊄B
Complement of Set A
A’
Intersection of sets A and B
A⋂B
Union of sets A and B
A⋃B
1
C) Equal Sets

2 sets A and B are equal i.e. A = B if they have exactly the same elements.
Ex : A = { 2, 1,
]then A = B
4} and B = { 1,
2, 4}
D) Subsets
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If every element of a Set A is also an element of a Set B , then A is a subset of B,
i.e. A ⊆ B.

If
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The Venn diagram below represents A ⊂ B
A ⊆ B. and A ≠ B, then A is a proper subset of B. i.e. A ⊂ B
𝜀
B
A
2
D) Universal Sets and Empty Sets

The Universal Set usually denoted by 𝜀, is the set that contains all the elements
considered in a particular problem.

An Empty Set, denoted by ∅ or { } has no elements.
Ex : If A = { x : x is a positive integer, x2 = 3 }, then A = ∅

The empty set is a subset of every set A . Thus, ∅ ⊆ A ⊆ 𝜀
E) Complement of a Set
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The complement of a Set A ( that’s A’) is the set of elements in the universal set
𝜀 that does not belong to the set A.

Ex :
If 𝜀 = { 5, 6, 7, 8, 9} and A = { 7, 9}, then A’ = { 5, 6, 8}
In set notation, A’ = { x : x ∈ 𝜀, and x ∉ A}

The shaded region in the Venn diagram below represents A’ :
𝜀
A’
A
3
F) Intersection of Sets

The intersection of 2 sets A and B is the set of all elements that belong to both A
and B, i.e. A ⋂ B
Ex :
If A = { 4, 6, 8, 10} and B = { 5, 6, 8}, then A ⋂ B = { 6, 8}
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In set notation, A ⋂ B = { x : x ∈ A and x ∈ B}
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The shaded region in the Venn diagram below represents A ⋂ B
𝜀
A

B
When the 2 sets A and B have no common elements, they are called disjoint sets
and A ⋂ B = ∅
4
G) Union of Sets
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The union of 2 sets A and B (i.e. A ⋃ B) is the sets of all elements that belong to
A or B or both.
Ex :
If A = { 1, 3 , 5} and B =
[ 2, 3, 4], then A ⋃ B = { 1, 2, 3, 4, 5}
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In set notation, A ⋃ B = { x : x ∈ A or x ∈ B}
The shaded region region in the Venn diagram below represents A ⋃ B
𝜀
A
5
B