CHAPTER - 01
SET THEORY
Important Notes
● What are the different categories and properties used to classify
sets?
❖ Definition of a Set:
★ A set is basically defined as a group of well-defined information. This information
is usually of a "similar type".
★ Examples provided are a set of all boys in a class, a set of all girls, a set of
vowels {A, E, I, O, U}, or a set of consonants.
❖ Basic Components and Properties:
1. Elements: The individual elements inside the curly braces {} of a set are referred
to as the elements of the set. The elements of a set are never repeated.
2. Cardinality (or Cardinal Number): This is one of the major properties of a set.
The cardinality of a set is the quantity of elements that are present in it. It is
represented by n(Set Name), e.g., n(A). Taking set A = {A, E, I, O, U} as an
example, the cardinality n(A) would be 5.
❖ Methods of Representation:
★ The sets can be represented by curly braces { }.
★ Two chief methods of representation are dealt with:
1. Listing Method: Simply list all elements of the set inside curly brackets. For
instance, set A = {1, 2, 3, 4}.
2. Set Builder Form: Create a formula or rule describing properties of elements
belonging to the set. For instance, set A may be described as {x | x ∈ Natural
Numbers, 1 ≤ x ≤ 4}.
❖ Types of Sets (Categories based on content/cardinality):
1. Empty Set (Null Set or Void Set): This refers to a set that has no elements. Its
cardinality is always zero. It is denoted by the symbol Φ or {}. An example is the
set of all boys in an all-girls school.
SET THEORY
Important Notes
● What are the different categories and properties used to classify
sets?
❖ Definition of a Set:
★ A set is basically defined as a group of well-defined information. This information
is usually of a "similar type".
★ Examples provided are a set of all boys in a class, a set of all girls, a set of
vowels {A, E, I, O, U}, or a set of consonants.
❖ Basic Components and Properties:
1. Elements: The individual elements inside the curly braces {} of a set are referred
to as the elements of the set. The elements of a set are never repeated.
2. Cardinality (or Cardinal Number): This is one of the major properties of a set.
The cardinality of a set is the quantity of elements that are present in it. It is
represented by n(Set Name), e.g., n(A). Taking set A = {A, E, I, O, U} as an
example, the cardinality n(A) would be 5.
❖ Methods of Representation:
★ The sets can be represented by curly braces { }.
★ Two chief methods of representation are dealt with:
1. Listing Method: Simply list all elements of the set inside curly brackets. For
instance, set A = {1, 2, 3, 4}.
2. Set Builder Form: Create a formula or rule describing properties of elements
belonging to the set. For instance, set A may be described as {x | x ∈ Natural
Numbers, 1 ≤ x ≤ 4}.
❖ Types of Sets (Categories based on content/cardinality):
1. Empty Set (Null Set or Void Set): This refers to a set that has no elements. Its
cardinality is always zero. It is denoted by the symbol Φ or {}. An example is the
set of all boys in an all-girls school.
