Chapter 1 Set Theory ,Relation, Functions

Cbse class 11th set notes

Set Theory , Functions and Natural Numbers

1. SET: 

• A set is a collection of well-defined objects, called elements or members of the set.
• These elements may be anything like nmbers ,letters of alphabets, points etc.
• Sets are denoted by capital letters and theirs elements by lower case letters.
• If an object  x is an element of set A, we write it as x∈A and read it as 'x belongs to A' other wise x does not belongs to A.

 Types of Set:

Finite Set:- 

A set which consist finite number of elements is called finite set.

Infinite  Set:-

A set which consist infinite number of elements is called infinite Set.

Singleton Set:-

A set which has consist only one element is called singleton set.

Null Set:-

A  set which contains no element at all is called null set.

It is also known as empty or void set.

It is denoted by {} or Φ.

Subset:-

Let A and B be two sets , if every elements of A belongs to B i.e., if every elements of set A is also an element of set B , then A is called subset of B andit is denoted by      A⊆B.

Super Set:-

If A is subset of a set B , then B is called superset of A. 

Proper Subset:-

Any subset A is said to be proper subset of another set B, if there is at least one element of B which does not belong to A, i.e, if A⊆B but A is not equal to B.

Equal Set:-

Disjoint Set:-

Types of Operation on SETs:-

1. UNION:-

2. INTERSECTION:

3.COMPLEMENT:

Relation in set :  Let A and B be two non empty sets, then R is relation From A to B if R is subset of A x B and is set of ordered pair (a,b) where  a belongs A and b belongs to B . It is denoted by aRb and read as " a is related to b by R".R= { (a,b):a∈A, b∈B, aRb}

Properties of Relation:-

• Reflexive Relation
• Irreflexive Relation
• Non-reflexive Relation
• Symmetric Relation
• Asymmetric Relation
• Antisymmetric Relation
• Transitive Relation

Function:-  

Let X and Y be two non-empty set . A function from X to Y isa rule that assign to each element x ∈ X a unique element y ∈Y.

If f is a function from X to Y we write f:X→Y. 

Function are denoted by f,g,h,i etc.

Domain and co-domain  of function:-    

Let f be a function from X to Y . Then set X is called domain of function f and Y is called co-domain function f.

Range of Function :-

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Dstl and cbse notes

It is denoted by A⊂B.