Venn diagram:
The diagrams drawn to given sets are known as Venn diagrams or Eule -Venn diagrams. Here we show the universal set U by points within rectangle and the subset A of the set U shown by the inner sector of a circle. If a set A is a subset of a set B then the circle showing A is drawn under the circle showing B. If A and B are not equal but they have some similar elements, then to show A and B by two intersecting circles.
![179_venn digram.png](https://www.expertsmind.com/../CMSImages/179_venn digram.png)
Problem : A class has 175 students. The given table defines the number of students studying one or more of the subsequent subjects in this case
Subjects No. of students
Mathematics 100
Physics 70
Chemistry 46
Mathematics and Physics 30
Mathematics and Chemistry 28
Physics and Chemistry 23
Mathematics, Physics and Chemistry 18
How many students are study Physics alone, Mathematics alone and Chemistry alone? Are there students who have not taken any one of these subjects?
Solution: Let P, C, M shows the sets of students taking Physics, Chemistry and Mathematics respectively. Let a, b, c, d, e, f, g shows the number of students defined in the bounded region as presented in the diagram then
a + d + e + g = 70
c + d + f + g = 100
b + e + f + g = 46
d + g = 30
e + g = 23
f + g = 28
g = 18
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![2043_venn digram1.png](https://www.expertsmind.com/CMSImages/2043_venn%20digram1.png)
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after calculating we get g = 18, f = 10, e = 5, d = 12, a = 35, b = 13 and c = 60
∴ a + b + c + d + e + f + g = 153
So, the number of students who have not studied any of these three subjects = 175 -153 = 22
Total number of students studying Mathematics only, c = 60
Total number of students studying Physics only, a = 35
Total number of students studying Chemistry only, b = 13.
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