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# What is Set in mathematics? Explained with examples

June 6, 2022 written by Azhar Ejaz

Definition of set

Set is a collection of well-defined and distinct objects.

Set is denoted by capital letters (A, B, C…). The member of sets are represented by small letters.
Sets are enclosed in curly brackets.

Give it a go

Introduction to operation of set

Properties of sets

## Methods to write a set

There are three methods of sets.

1. The Descriptive Method.

2. The Tabular Method.

3. Set builder Method.

### The Descriptive Method:

In the descriptive method, the set is represented in words.

For Example:

The set of natural numbers.

The set of alphabets.

### The Tabular Method

In the tabular method, sets are represented by elements within braces. For example.

N = {1, 2, 3, 4, …}

A = {apple, banana, mango}

### Set builder Method

Setbuilder notation is a mathematical notation to describe a set by representing its elements or explaining the properties that its members must satisfy.

For Example:

A= {x|x is first ten natural number}

B= {x|x ∊ N ∧ x ≤ 5}

## Types of set

There are different types of sets.

### Empty Set

A set having no elements. It is denoted by the symbol ∅ and {}

For Example: A= {}, B=∅

### Singleton Set

A set having only one element is called a singleton set.

For Example: A= {1}, B= {2}, C=a {a}

### Finite Set

Finite set has limited number of elements.

For example: N = {1, 2, 3, 4, 5}, N= {x|x ∊ N ∧ x ≤ 5}

### Infinite Set

An infinite set has an unlimited number of elements. For example:

W= {0, 1, 2, 3, …}

Set of all integers.

### Equal Set

Two or more sets are said to be equal sets if they have the same number of elements and same elements then set A is equal to set B and set B is equal to set A.

A= {a, b, c, d}, B= {a, b, c, d} Here, n(A)=n(B) and also have same elements.

### Equivalent Set

Two or more sets are said to be equivalent sets if they have the same number of elements but not the same elements then set A is equivalent to set B and set B is equivalent to set A. For example:

A= {1, 2, 3, 4}, B= {a, b, c, d}

In these sets n(A) = n(B), but have not same elements.

### Subset

If A and B are two sets, set A is said to be a subset of set B if all the elements of set A belong to set B. The symbol of the subset is “⊆”.

For example:

A= {1, 2, 3, 4} , B= {1, 2, 3, 4, 5, 6, 7}

A ⊆ B

If A and B are two sets, set B is said to be a subset of set A  if all the elements of set B belong to set A. For example:

A= {a, b, c, d, e, f} , B= {c, d, e, f}

B⊆A

### Universal Set

A universal set is a set that has elements of all the related sets without any repetition of elements. A universal set is denoted by U. For example. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A {1, 3, 5, 7, 9} , B= {2, 4, 6, 8}

### what is set?

A set is a collection of well defined and distinct objects. The objects in a set are called elements, Set is denoted by capital letters (A, B, C…). The member of sets are represented by small letters.
Sets are enclosed in curly brackets.
For example:
A= {1,2,3,4} is a set of numbers

### What are types of set

There are different types of sets.
Empty set
Singleton set
Finite set
Infinite set
Equal set
Equivalent set
Subset
Universal set

### what are the element of the set?

The elements of sets are the numbers, objects, symbols, etc. that are contained in a set. For example, in the set A={12,33.56}, 12, 33 and 56 are the elements of sets.

### Method to write a set

There are three methods to write a sets.
1. The Descriptive Method.
2. The Tabular Method.
3. Set builder Method.

### what is empty set?

A set having no elements. It is denoted by the symbol ∅ and {}
For Example: A= {}, B=∅

### what is Singleton Set?

A set having only one element is called a singleton set.
For Example: A= {1}, B= {2}, C=a {a}

### what is Finite Set

Finite set has limited number of elements.
For example: N = {1, 2, 3, 4, 5}, N= {x|x ∊ N ∧ x ≤ 5}

### what is infinite Set

An infinite set has an unlimited number of elements. For example:
W= {0, 1, 2, 3, …}
Set of all integers.

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