. A class has 175 students. Following is the description showing the number of students studying one or more of the following subjects in this class

Mathematics 100, Physics 70, Chemistry 46; Physics and Chemistry 23; Mathematics and Physics 30; Mathematics and Chemistry 28; Mathematics, Physics and Chemistry 18. 

How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone? Are there students who have not offered any of these three subjects. 


Best Answer

Answer: Let A, B and C denote the sets of students studying Mathematics, Physics and Chemistry  respectively.

Let us denote the number of elements (students) contained in the bounded region as shown in the diagram by a, b, c, d, e, f and g respectively.



So, the number of students who have not offered any these three subjects 

175 – 153 = 22

Students studying Mathematics only = a = 60

Students studying Physics only = b = 35

Students studying Chemistry only = c = 13



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