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1. Venn Diagrams
A Venn Diagram shows the relationship between groups of different things in a visual way. These groups are known as sets. Using Venn diagrams allows us to sort data into two or three circles which overlap in the middle. Each circle follows a specific rule, so any numbers or objects placed in the overlapping part follow both rules. A typical Venn diagram looks like the picture below.
Interpreting the Venn Diagrams
Case I. For two circles
Total = Elements in A only + Elements in B only + Elements in A and B
Case II.
For three circles
Total = Only A + Only B + Only C + (A and B) + (B and C) + (A and C) + (A and B and C)
1.1. Examples on Venn Diagrams
Example:
Out of 50 students, 15 are taking only Maths, and 18 are taking only the Science exam. 5 students take both exams. How many students take neither Maths nor Science exam?
Solution:
Number of Students choosing neither Maths nor Science = 50 -(15 + 5 + 18)
= 50 - 38
= 12
Example:
A survey has been conducted in a class regarding their favourite superhero. The results are represented in the form of a Venn diagram shown below. How many students like only Spiderman?
Solution: From the Venn diagram:
Number of students like only Spider man is 25 as shaded in the Venn diagram.
