Out of 100 students, 15 passed in English, 12 passed in Mathmatics, 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.

Explanation

To solve the problem, we will use the principle of inclusion-exclusion and a Venn diagram to visualize the relationships between the sets of students passing in different subjects.

Let's denote:
- \( E \): the set of students who passed in English
- \( M \): the set of students who passed in Mathematics
- \( S \): the set of students who passed in Science

From the problem, we have the following information:
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