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A set is a well-defined collection of objects.

By well-defined collection, we mean that we should be able to decide whether a particular object belongs to a definite collection or not.

Example of a well-defined collection is natural numbers less than five. This collection of natural numbers is well defined, as we can definitely decide whether a given particular number belongs to this collection or not.

An example of a set that is not well defined is a set that consists of clever students. This is a not a well-defined set because the choice of clever students is not clear, since there is no accurate measure for cleverness.

A set is denoted with a capital letter.

E.g.: A, Q, S

The elements of a set are denoted with small letters.

e.g.: x, p, s, etc.

The word **element** is used synonymously with the words object and member.

**A= {p, q, r}**

The element p belongs to set A.

p âˆˆ A

z âˆ‰ A

**N : The set of natural numbers**

**Z : The set of integers**

**Q : The set of integers
R : The set of real numbers
Z**

There are two ways of representing sets.

1. Roster form

2. Set-builder form

This method of representing sets is also called the tabular form.

Ex: Prime numbers less than 10.

Similarly, a set of natural numbers between 20 and 30 is represented as:

The order of the elements in a set is unimportant.

While representing a set in roster form, the elements are generally not repeated. Only distinct elements are written while representing a set in roster form.

The set-builder form is a more concise form of a given set.

To write the set in the set-builder form, start with a bracket and write the variable.

Then a colon is placed and a property is assigned to this number.

Ex 1: {2, 3, 5 and 7} is written in set-builder form as P =

The set is named as P and read as P is the set of all x such that x is a prime number less than 10.

Ex 2: Represent the set of natural numbers between 20 and 30 using the set-builder form.

Set of natural numbers between 20 and 30 = {21, 22, 23, 24, 25, 26, 27, 28, 29}

We name this set A.

A = {n:n is a natural number, 20 < n < 30}

This is read as: A is the set of all n such that n is a natural number and n is lies between 20 and 30.

A set is a well-defined collection of objects.

By well-defined collection, we mean that we should be able to decide whether a particular object belongs to a definite collection or not.

Example of a well-defined collection is natural numbers less than five. This collection of natural numbers is well defined, as we can definitely decide whether a given particular number belongs to this collection or not.

An example of a set that is not well defined is a set that consists of clever students. This is a not a well-defined set because the choice of clever students is not clear, since there is no accurate measure for cleverness.

A set is denoted with a capital letter.

E.g.: A, Q, S

The elements of a set are denoted with small letters.

e.g.: x, p, s, etc.

The word **element** is used synonymously with the words object and member.

**A= {p, q, r}**

The element p belongs to set A.

p âˆˆ A

z âˆ‰ A

**N : The set of natural numbers**

**Z : The set of integers**

**Q : The set of integers
R : The set of real numbers
Z**

There are two ways of representing sets.

1. Roster form

2. Set-builder form

This method of representing sets is also called the tabular form.

Ex: Prime numbers less than 10.

Similarly, a set of natural numbers between 20 and 30 is represented as:

The order of the elements in a set is unimportant.

While representing a set in roster form, the elements are generally not repeated. Only distinct elements are written while representing a set in roster form.

The set-builder form is a more concise form of a given set.

To write the set in the set-builder form, start with a bracket and write the variable.

Then a colon is placed and a property is assigned to this number.

Ex 1: {2, 3, 5 and 7} is written in set-builder form as P =

The set is named as P and read as P is the set of all x such that x is a prime number less than 10.

Ex 2: Represent the set of natural numbers between 20 and 30 using the set-builder form.

Set of natural numbers between 20 and 30 = {21, 22, 23, 24, 25, 26, 27, 28, 29}

We name this set A.

A = {n:n is a natural number, 20 < n < 30}

This is read as: A is the set of all n such that n is a natural number and n is lies between 20 and 30.