This document introduces John Venn and Venn diagrams, which are diagrammatic representations used to visualize relationships between sets and set operations. It defines key concepts in set theory including the universal set, complement of a set, union of sets, intersection of sets, and difference of sets. Venn diagrams use circles to represent sets and the areas where the circles overlap to demonstrate relationships between the sets.

2. SET OPERATIONS
-BY
JOHN VENN

3. AUTHOR INTRODUCTION
John venn (1834-1883) a british mathematician
used diagrammatic representation as an aid to
visualize various relationships between sets and
set operations.

4. venn diagrams
 We use diagrams or pictures in geometry to
explain a concept or a situation and sometimes we
also use them to solve problems.
 In mathematics, we use diagrammatic
representations called venn diagrams to visualise
the relationships between sets and set operations.

5. THE UNIVERSAL SET
Sometimes it is used to consider a set which
contains all elements pertinent to a given
discussion.
The set contains all the elements under
consideration in a given discussion is called the
UNIVERSAL SET. The universal set is denoted by U
or .
FOR EXAMPLE, if the elements currently under
discussion are integers , then the universal set U is
the of all integers. i.e., U={n:nZ}

6. COMPLEMENT OF A SET
The set of all elements of U (universal) that are
not elements of A  U is called the complement of
A.
The complement of A is denoted by A or A.
READING NOTATIONS
In symbol, A = {x:x U and x A}.
EX: Let U={a,b,c,d,e,f,g,h} & B={b,d,g,h}.
Then A={a,c,e,f}

7. UNION OF TWO SETS
The union of two sets A and B is the set of
elements which are in A or in B or in both A and
B. We write the union of sets A and B as AUB.
READING NOTATION:
U- Union.
Read AUB as ‘A union B’
In symbol, AUB = {x:xA or xB}.
EX: Let A={11,12,13,14} & B={9,10,12,14,15}.
Then AUB={9,10,11,12,13,14,15}

8. INTERSECTION OF TWO SETS
 The intersection of two sets A and B is the set of
all elements common to both A and B. We denote
it as AB.
READING NOTATION:
 - Intersection.
Read AB as ‘A intersection B’
Symbolically, we write AB ={x:xA and xB}.
EX: Let A={a,b,c,d,e} & B={a,d,e,f}.
AB= {a,d,e}.

9. DIFFERENCE OF TWO SETS
The difference of the sets A and B is the set of all
elements belonging to A but not to B.
 The difference of the two sets is denoted by A-B or
A/B.
READING NOTATION:
A-B or A/B = A difference B.
In symbol , we write: A – B ={x:xA and xB}
Similarly, we write:B – A ={x:xB and xA}
EX: Consider the sets A={2,3,5,7,11} & B={5,7,9,11,13}.
A-B ={2,3}

10. THANYOU