Formulas For Venn Diagrams
Formulas for Venn Diagram
When a collection of given sets is given. To find the all possible relations between sets , we draw Venn Diagram i.e. Venn Diagram is the representation to find the all logical relations between different sets.
Definition and use of Venn Diagrams:-
- Definitions: Venn diagram, also known as Euler-Venn diagram is a simple representation of sets by diagrams.
- Venn diagram representing mathematical or logical sets pictorially as circles or closed curves within a rectangle.
- The usual picture makes use of a rectangle as the universal set and circles for the sets under consideration.
Basic Formula for the Venn Diagram
- Some basic formulas for Venn diagrams of two and three elements.
- n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
- n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)
- And so on, where n( A) = number of elements in set A.
- After understanding the concept the of venn diagram with diagram, we don’t have to remember the formulas.
Venn Diagram for 2 sets
n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
X = number of elements that belong to set A only
Y = number of elements that belong to set B only
Z = number of elements that belong to set A and B both (A ∩ B)
W = number of elements that belong to none of the sets A or B
From the above figure, it is clear that
n(A) = x + z ;
n (B) = y + z ;
n(A ∩ B) = z;
n ( A ∪ B) = x +y+ z.
Total number of elements = x + y + z + w
Venn Diagram for 3 sets
n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)
W = number of elements that belong to none of the sets A, B or C