Operations on sets- Venn diagrams

1. VENN DIAGRAMS
Mrs.Mahitha Davala
M.Com.,APSET.,M.B.A

2. Swiss mathematician Euler and British mathematician John-Venn gave idea of
representing set through pictures.
The diagrams drawn to represent sets are called Venn-Euler diagrams or simply
Venn diagrams.
In Venn diagrams the universal set U is represented by points within a rectangle
and its subsets are represented by points closed (usually circles) within the
rectangle .

3. Operation on Sets
Union of Sets: Let A and B be two sets. The union of A and B is the set of all those
elements which belong to A or to B or to both A and B.
Thus AUB={x:x⊂A or x⊂B}
Clearly x∈AUB⟺x∈A or x∈B
And x∉AUB⟺x∉A or x∉ B.
⊂
⊂⊂⊂⇒⇒

4. Intersection of Sets: Let A and B be two sets. The intersection of A and B is the
set of all those elements that belong to both A and B
The intersection of A and B is denoted by A⋂B
A⋂B = {x:x∈A and x∈B}
Clearly, x∈A⋂B⟺x∈A and x∈B.
Disjoint Sets: Two sets A and B are said to be disjoint if
A⋂B=Ø

5. Difference of Sets: Let A and B be two set. The difference of A and B, written as
A-B, is the set of all those elements of A which do not belong to B.
Thus A-B={x:x∈A and x∉B}
Similarly the difference B-A is the set of all those
elements of B that do not belong to A

6. Symmetric Difference of two sets: Let A and B be two sets. The symmetric
difference of sets A and B is the set (A-B)U(B-A) and is denoted by A∆B.
Thus A∆B=(A-B)U(B-A)={x:x∉A⋂B}
Complement of a Set: Let U be the universal set and let A be a set such that A⊂U.
Then, the complement of A with respect to U is denoted by Ac or A’ or U-A and is
defined as the set of all those elements of U which are not in A

7. Thank You