Formulas For Venn Diagrams
Formulas For Venn Diagrams:-
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 in case of two elements.
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 (AB)
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 in case of three elements.
W = number of elements that belong to none of the sets A, B or C