Venn diagrams are used to represent relationships between sets. They can show disjoint sets with no common elements, overlapping sets that share some elements, unions that combine elements, intersections that show only shared elements, complements that show elements not in the given set, and subsets where all elements of one set are contained within another set. Key elements of Venn diagrams include circles to represent sets, shading to indicate elements in operations like unions and intersections, and a universal set that contains all elements being considered.

1. SETS
VENN DIAGRAMS

2. Disjoint Sets
A
B
No common elements in both Sets

3. Overlapping Sets
A
Common
Elements
B

4. ξ
A
B
ξ = Universal Set(also called parent set)
contains all sets to be discussed

5. Union of Disjoint Sets
ξ
A
B
A⋃B
Both Sets will be shaded

6. Intersection of
Disjoint Sets
ξ
A
B
A⋂B
No region will be shaded

7. Union of Overlapping Sets
ξ
A
B
A⋃B
Both sets will be shaded

8. Intersection of
Overlapping Sets
ξ
A
Common Region
B
A⋂B
Only common region will be shaded

9. Complement of Set A
ξ
A
B
A’
All regions other than “A” will be shaded
(Shaded in Blue)

10. Complement of Set A
ξ
A
B
A’
All regions other than “A” will be shaded
(Shaded in Blue)

11. Subset of Set A
ξ
A
B
B is sub set of set A
(All elements in set B have been taken
from set A )

12. Subset of Set A
ξ
A
B
B is sub set of set A
(All elements in set B have been taken
from set A )

13. Complement of Set B
B’
ξ
A
B
All regions other than “B” will be
shaded (Shaded in Blue)