A class has 175 learners. The given table describes the number of learners 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 learners are study Physics alone, Mathematics alone and Chemistry alone? Are there learners who have not taken any one of these subjects?
Ans) Let P, C, M shows the sets of learners taking Physics, Chemistry and Mathematics correspondingly.
Let a, b, c, d, e, f, g represents 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
After measuring 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 learners who have not studied any of these 3 subjects
= 175 -153 = 22
Total number of learners studying Mathematics only, c = 60
Total number of learners studying Physics only, a = 35
Total number of learners studying Chemistry only, b = 13.