SETS-class 11-maths-notes

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}

 

 

 

 

 

 

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