### Venn Diagram

# A Venn diagram is a simple representation of sets by diagrams.

# The usual depiction makes use of a rectangle as the universal set and circles for the sets under consideration.

In competitive exams, questions asked from this topic involve 2 or 3 variables.

Let's take a look at 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 )

where _{n}(A) = number of elements present in set A.

_{ n}(B) = number of elements present in set B.

_{ n}(A ∪ B) = number of elements present in either set A or B.

_{ n}(A ∩ B) = number of elements present in both set A and B.

Example: In a class, 60% of students can speak English, 75% of students can speak Hindi, If 40% of students can speak both, how much percentage of students can speak at least one language? How much percentage of students speak neither English nor Hindi?

Explanation: _{n}( A ∪ B) = _{n}(A ) + _{n}( B ) -_{ n}(A∩ B)

_{n}(A ∪ B) = 60 + 75 - 40 = 95%

95% of students can speak at least one of the language.

100% - 95% = 5% of students speak neither of the two languages.