Question

Every student in a class of 42 students, studies at least one of the subjects,
Mathematics, English and Econonmics, 14 students study Mathematics, 20
Economics and 24 English, 3 students study Mathematics and Economics, 2 English
and Eeonomics and there is no student who study all the three subjects. Find the
number of students who study Mathematics but not Economics.
(Ans 3)​

Answer 1

With the answer given below question, I asse your question is to find the number of students who studied math but not English as discussed below:

let

n(m) be number of students who studied math

n(en). for English students and

n(ec) for economics student

given

n(mUenUec) = 42

n(m) = 14

n(ec) = 20

n(en) = 24

n(m and ec) = 3

n(en and ec) = 2

n(m and en and ec) = 0

now number of students who studies mathmatics but not economics = n(m) - n(m and ec)

we have n(m) and n(m and ec), so the answer would be 14 - 3 = 11.

but consider the variety of information provided and the thing that we can derive using the information i.e. n(m and en) (number of students who studied both math and English) which is not given, I. think our question part is to find number of students who studied math but not ENGLISH .

the required number would be n(m) - n(m and en)

we have n(m but we need to derive n(m and en)

now

n(mUenUec) = n(m) + n(en) + n(ec) - n(m and en) - n(m and ec) - n(en and ec) + n(m and en and ec)

42 = 14 + 20 + 24 - n(m and en) - 3 - 2 + 0

42 = 53 - n(m and en)

n(m and en) = 53 - 42 = 11

so the number of students who studied math but not english = 14 - 11 = 3