# Venn Diagrams

A venn diagrams is merely a closed figure and the points of the interior of closed figure represent the elements of the set under consideration. Generally, a curve like an oval or a circle or rectangle is used to represent the sets.John Venn was a British Mathematician(1834- 1923) who developed the idea of using diagram to represent sets.

Leonhard Euler (1707- 1783) also used diagrams to represent sets. So these diagrams are also called a

**Venn-Euler diagrams.**

**Example :**

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} , A = { 1, 2, 5} and

B={1, 2, 3, 4, 5, 6} So A ⊂ B.

This can be represented by venn-diagram as follow :

**Practice Test**

Q.1 Represent the following by Venn-diagram.

1) Set A = { 6, 5, 4, 3, 2, 1}.

2) Set B = { x| x is a vowel in the word “THESAURUS”}.

3) Set P = { x| x ∈ N, x ≤ 8 }.

Q.2 Observe the Venn-diagram and then write the following in Set-Builder form :

1)

2)

3)

**Answers :**

Q.1 ----> 1)

2)

3)

Q.2 --->

1) A = { x| x ∈ N, x ≤ 5}

2) B = { x | x ∈ N, x is a multiple of 3 and x ≤ 15}.

3) C = { x | x is a vowels }

**Set Theory**

• Sets

• Representation of Set

• Cardinal Number

• Types of Sets

• Pairs of Sets

• Subset

• Complement of Set

• Union of the Sets

• Intersection of Sets

• Operations on Sets

• De Morgan's Law

• Venn Diagrams

• Venn-diagrams for sets

• Venn-diagrams for different situations

• Problems on Intersection of Two Sets

• Problems on Intersection of Three Sets

• Sets

• Representation of Set

• Cardinal Number

• Types of Sets

• Pairs of Sets

• Subset

• Complement of Set

• Union of the Sets

• Intersection of Sets

• Operations on Sets

• De Morgan's Law

• Venn Diagrams

• Venn-diagrams for sets

• Venn-diagrams for different situations

• Problems on Intersection of Two Sets

• Problems on Intersection of Three Sets