Q: Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed
(i) in English and Mathematics but not in Science
(ii) in Mathematics and Science but not in English
(iii) in Mathematics only
(iv) in more than one subject only
Let the set of students who passed in mathematics be M, the set of students who passed in English be E and set of students who passed in science be S.
Then n(U)=100, n(M)=12, n(S)=8,
and
According to the Venn diagram
Thus, number of students who passed in English and mathematics but not in science = d= 2
Number of students who passed in Science and mathematics but not in English = f=3
Number of students who passed in mathematics only = g =3
Number of students who passed in more than one subject = b+ e+ d +f =0+4+2+3 =9