Question

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 and 4 in all three. Find how many passes in English and mathematics but not science and find how many passed in mathematics and science but not in English and find mathematics only

Answer 1

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

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