# Class 6 Set

## Concept of a Set

A set is a well defined collection of objects. For example, collection of alphabets, collection of numbers, collection of books, collection of cities, etc.
In mathematical language we call these groups a ** Set**.

Let's see some valid example of sets.

1. A collection of even numbers.

2. A collection of odd numbers.

3. A collection of prime numbers.

4. A collection of number which are divisible by 3.

5. A collection of cities of India.

Some examples of invalid sets

1. A collection of good students in a school.

2. A collection of beautiful flowers in a garden.

3. A collection of healthy food.

4. A collection of good movies.

## Notation of a Set

Generally, sets are denoted by capital letters A, B, C, etc. Element of the sets are written in small letters a, b, c. etc. If 'a' is an element of set A, then it is written as a ∈ A.
It is read as ** a belongs to A**. If b is not a member of set B, then it is written as b ∉ B. It is read as

**.**

*b does not belongs to B*## Representation of Sets

Set can be represented in two ways.

1. Roster listing method

2. Set builder method

## Roster Listing Method

In this method we list all the members of the set, separating them by means of commas and enclosing them in curly brackets {}. Let's see some examples.

**Example 1.** P is a set consisting of element 2, 4, 6 and 8. Then we write P = {2, 4, 6, 8}.

**Example 2.** A is a set of prime numbers less than 10. Then we write A = {2, 3, 5, 7}.

**Example 3.** P is the set of vowels, then we write P = {a, e, i, o, u}.

## Set Builder Method

In this method, we write the set by some special properties satisfied by all its element. We write it as

A = {x : P(x)}

Or A = {x | x has the property P(x)}

It is read as A is the set of all elements 'x' such that 'x' has the property P

Let's see some examples.

**Example 1.** Y = {2, 3, 5, 7} is expressed as

Y = {x | x is a prime number less than 10}

**Example 2.** A = {2, 4, 6, 8, 10, 12, 14} is expressed as

A = {x | x is an even number less than 15}

**Example 3.** N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

N = {x | x is a natural number less than 15}

**Example 4.** B = {3, 6, 9, 12, 15, 18} is expressed as

B = {x | x is natural number divisible by 3 and less than 20}

## Types of Sets

Basically, there are 4 types of sets.

1. Finite set

2. Infinite set

3. Empty set

4. Singleton set

## Finite Set

A set having no element, or a definite number of elements is called a finite set. Let's see some examples.

1. A = {2, 4, 6, 8} = Set of even numbers less than 10.

2. B = {3, 5, 7, 9, 11} = Set of odd numbers less than 12.

3. C = {a, e, i, o, u} = Set of vowels in alphabet

## Infinite Set

A set having unlimited number elements is known as an infinite set. If we start counting all the elements one by one , the counting process will not come to an end. Let's see some examples.

1. P = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...} = Set of all natural numbers.

2. Q = {2, 4, 6, 8, 10, 12, 14, ...} = Set of all even numbers.

3. R = {2, 3, 5, 7, 11, ...} = Set of all prime numbers.

4. S = {0, 1, 2, 3, 4, 5, 6, ...} = Set of all whole numbers

## Empty Set

The set which contains no element is called the empty set. Let's see some examples.

1. The set of natural numbers, less than 1 is an empty set.

2. The set of days, starting with the letter 'a', is an empty set.

3. The set of odd numbers, divisible by 2 is an empty set.

## Singleton Set

The set which contains only one element is called a singleton set. Let's see some examples.

1. The set of even prime numbers {2}.

2. The set of days in a week, beginning with M.

3. The set of months in a year having 28 days {February}.

## Class-6 Set Test

## Class-6 Set Worksheet

## Answer Sheet

**Set-Answer**Download the pdf

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