Basic definitions and notation, types of sets, equality, and Venn Diagram

Name of Sets
Union of set	Sub-set	Proper
Difference set	Null	Set Of Sets
Complementary	Infinite	Singleton
Universal	Equal	Finite
Power

Set Definition :

A definite and distinct group of things called set. On other hand we can say that a well define group of things called set.

Representation of a Set:- with Method

We can represent set two types.

1):-Tabulation or roster method:- In this method all element write in middle bracket.

Example:- {1,2,3,4…..}

2):-property method or builder form:- In this method we define special property of element and write in the middle bracket.

Example:- S={1,2,3,4…}

S={ Where x:x is a positive number}

If we denote any se set by A then n(A) show its number of elements.

If A ={1,2,3,4}

Then n(A)=4

Types of Set and Definition Formula with examples and Solutions:-

1) Singleton set Definition :- When a set contain only one element its called singleton set.

Example:-S={5}

2) Finite set Definition :- When we can count all element of a set its called finite set.

Example:- A={4,5,6,7,8}

n(A)=5

3) Equal set Definition :- When two set contain same element then they called equal set.

A={14,16,20,5}   B={5,16,20,14}

Bothe set contain same element so they are equal set.

4)Infinite set Definition :- When a set contain infinite element which are not countable then that set called infinite set.

Example:-A={4,6,8,2,6,5………..}

5)Null set Definition with examples:- When a set contain zero element its called null set. This se denoted by {} and ф.

Example:- {x:x² =16 ; where x is a odd number} this is null set because 16 is even number square not a odd number square.

6)Sub-set examples with Definition :- When two set A and B And A’s all elements contain in B then we can say that A is the sub-set of B. and we denote it by

Example:-A={1,2,3,4}     B={5,1,6,2,3,4,7}

Important Points of Set:-

I]:-Every set is subset of itself.

II]:-Null set is subset of every set.

III]:-n elements set have 2ⁿ sub-set

7):-Proper Set Definition :- If A is the sub-set of B and B≠A it mean all elements of A are available in B but not all elements of B’s are available is A. so in this case we can say A is proper set.

Example:- A={1,2,3,4,……}  B={1,2,3,4,5,6……}  A is the proper set of B.

8):–Definition for Set Of Sets:- When elements of a set are set in itself then we can say this set is set of sets.

Example:-A={{1,2},{3,5},{7,8,9}} we can see A’s all elements are set in itself.

9):- Definition for Power set:-Set of sub-sets of a set called its power set.

Example:-A={1,2,3,4}

A’s subset={ф,{1},{2},{3},{4},{1,2}…….} this is the power set of A.

10):- Definition for Universal set:- If we have given sets particular case and they all are sub-set of a set then that set called universal set.

Example:-If U={1,2,3,4,5,6,7,8}

and A={1,2,5,6}  B={3,4,7,8}

it show u is the universal set of A and B.

11)Complementary set Definition :- If A is set and U is a universal set then set of these elements which are available in U but not in A called complementary set of A.

Examples for set:-A={1,5,3} U={1,2,3,4,5}

A’={2,4}

12)Difference set:-

Let we have two set A and B and question is aind the A-B then:-

A={1,2,3,4,5,,6} B={2,3,4}

Then A-B={1,5,6}

13):-Union of set of Definition :-

Let we have two set A={1,2,3,4} and B={4,5,6}

Then A B={1,2,3,4,5,6}

14):-Definition of Intersection of set:-

Let we have two set A={6,5,7,8,9} and B={1,2,6,7}

Then A ={6,7}

Set Theory Formula:-

Positive numbers set denoted by I⁺ .

Negative numbers set denoted by I^– .

Set Theory Examples with solutions

Example:-In 6000 people 3500 people read English news paper 2500 people read Hindi and 800 people read both news paper then how many people does not read news paper?

Solution:- Given U=6000,n(E)=3500 ,n(H)=2500 ,n(E∩H)=800

=6000-{(3500+2500)-800}

=800 people does not read any news paper.

Example:-In 100 people 60 people drink coffee and 70 people drink tea then how many person drink both coffee and tea?

Solution:-U=100, n(T)=70, n(C)=60

Then n(T∩C)=(70+60)-100

=30 people drink both.

Example:-IF P=(1,3,5,6,7,8,9} A={1,2,3,4} B={3,4,5,6,9}

Find the (AUB)’.

(AUB)={1,2,3,4,5,6,9}

Then (AUB)’=P-(AUB)

={7,8}

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