Question

Out of 50 students, 15 passed in
English, 12 passed in
Mathematics, 8 in Science, 6 in
English and Mathematics, 7 in
Science and Mathematics, 4 in
English and Science and 4 in all
three.
How many students passed in
Science and Mathematics but not
in English?​

Answer 1

Step-by-step explanation:

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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