Questions on Venn Diagram
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.
