Page 74 - ICSE Math 8

6 Set Theory

Key Concepts

• Set • Subset of a Set
• Representation of Sets • Operations on Sets
• Types of Sets • Complement of a Set
• Cardinal Number of a Set

Set

You know that set is a collection of well-defined and distinct objects. These objects are called the elements of
the set or the member of the set. A set is represented by capital letters like A, B, X, Y, etc., and small letters
like a, b, x, y, etc., are used to represent the elements of a set. For example, A = {1, 2, 3,4, 5}, here A is a set
of numbers containing elements (1, 2, 3, 4, 5).
The symbol ‘∈’ stands for ‘belongs to’ and ‘∉’ stands for ‘does not belong to’. If an object is an element of a
set, then we say it belongs to that set. For example, if D is the set of days of a week, then Monday is one of
the elements of set D and we say Monday belongs to D or MONDAY ∈ D. We can also say that JUNE ∉ D.
There are certain symbols that are used (fixed) to represent some special sets. They are as follows:
N → Set of all natural numbers
W → Set of all whole numbers Maths Info
Z → Set of all integers
Q → Set of all rational numbers The theory of sets was developed by
German mathematician Georg Cantor.
R → Set of all real numbers

Do not use these special symbols to represent any other set.

Representation of Sets

A set can be represented in two forms.
(a) Roster or Tabular form (b) Set-builder or Rule form

Roster or tabular form
In this form, the elements of a set are written by enclosing them in curly brackets { } and separating two
elements by a comma. For example, the set D of days of a week can be written as
D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Points to remember

• Elements in a set cannot be repeated.
• In a set, elements can be written in any order.
Example 1: Write the set of letters of the word ALLAHABAD in the roster form.

Solution: Let us denote the set by C.
So, C = {A, L, H, B, D}

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