Let M be the set of students who passed in Mathematics, E be the set of students who passed in English and S be the set of students who passed in Science.
Given n (U) = 100,
n(E) = 15, n(M) = 12, n(S) = 8,
n(E ∩ M) = 6, n(M ∩S) = 7, n(E ∩ S) — 4, and n(E ∩ M ∩ S) = 4,
Number of students passed in English and Mathematics but not in Science = b = 2
(ii) Number of students passed in Mathematics and Science but not in English = d = 3
(iii) Number of students passed in Mathematics only = e = 3
(iv) Number of students passed in more than one subject = a + b + c + d =4+2+0+3=9