**SETS**

**A Set is a collection of Well-defined Objects.**

By “**Well-defined**” we mean to say that it should be possible for us to clearly define whether an object belongs to a collection or not.

A set is denoted by uppercase letters/capital letters. For example: A, B, C, X, Y, Z, etc.

**Objects** of a set are called **elements** or **members** of a Set. It is denoted by lowercase letters/small letters. Elements are enclosed inside **curly braces {}.**

**A set of odd numbers less than 10.**

**A = {1,3,5,7,9}**

** Elements of a Set**

**Name of a Set**

**Identifying a collection whether it is a Set or not.**

**(i) A Set of rivers of India: **It is a Set as it is a well-defined collection and same for all. That means it does not vary from person to person.

**(ii) A set of best actors: **It is **NOT **a Set as it is not a well-defined collection. It varies from person to person.

**REPRESENTATION OF A SET**

**ROSTER FORM****SET-BUILDER FORM**

**ROSTER FORM: **In Roster Form, all the elements of the Set, separated by commas, are enclosed within the curly brackets.

**For Example:** The set of prime numbers less than 10 is represented in **Roaster Form** as,

**{2,3,5,7}**

**SET-BUILDER FORM: **In a Set-builder form, a variable, say x, is used to represent the elements of the set, and property or a rule is given which is satisfied by the elements of the set.

If **A is a set** consisting of **elements x** satisfying the **Property P**, then we write,

A= {x:x satisfies property P}.

The above statement is read as **“A is the set of all x such that x satisfies property P”.**

**The symbol ‘:’ or ‘|’ means ‘such that’**

**For Example: **The set of odd numbers less than 10.

A={x|x is an odd number less than 10}

Or

A={x|x=2n+1, n∈W, n<10}

** **