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Sets

Chapter Seven

Sets
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Introduction

Objects exist in different categories and characteristics which sometimes may be Mathematics for Secondary Schools
difficult to describe and understand their nature. Understanding the concepts of sets
simplifies the process of categorising and organising such objects based on their
nature. In this chapter, you will learn the concept of a set, distinguish between types of
sets, perform operations with sets, represent sets in Venn diagrams, and determine the
number of elements in a set. The competencies developed will enable you to simplify,
categorise, analyse, and generalise different problems arising from real-life situations
more systematically.

Think
Organising and categorising data with little or no knowledge about the
concepts of sets.

Concept of a set Engage in Activity 7.1 to explore how to
A set is a collection of well defined objects form sets in real life.
with common and distinct features. The
objects in a set are are called elements Activity 7�1: Sorting items having the
or members of the set. The members of same characteristics
a set are usually separated by commas 1. Gather a variety of items such
and enclosed within curly brackets { }. as exercise books, pens, pencils,
For instance, if B is a set representing erasers, rulers, notebooks,
students in a class and John is a student in highlighters, and paperclips.
that class, then John is a member of set B 2. Sort the items based on their specific
or is an element of set B. This relationship characteristics.
is denoted by the symbol ∈, which means 3. How many different groups of items
‘a member of’ or ‘an element of’. That is, have you created?
John ∈ B. 4. Assign each group a letter: A, B, C,


For example, if C = 1, 2, 3 , then 1∈ etc.
C, 2∈C and 3∈C where as 5  C (5 is not 5. Reflect on the similarities and
an element of C). The number of distinct differences between the groups.
elements in set A is represented by n(A). Consider the characteristics that
For example, if A =  a, e, i, o, u , then influenced your sorting decision.
n(A) = 5.

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