In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4, French and Sanskrit = 5, English , French and Sanskrit = 3. Find the number of students who study
(i) only French, (ii) only English.
(iii) only Sanskrit. , (iv) English and Sanskrit but not French.
(v) French and Sanskrit but not English.
(vi) French and English but not Sanskrit.
(vii) atleast one of the three languages.
(viii) none of the three languages.

Explanation

To solve the problem, we will use the principle of inclusion-exclusion and Venn diagrams. Let's denote:
- \( F \): the set of students studying French
- \( E \): the set of students studying English
- \( S \): the set of students studying Sanskrit

Given data:
- \( |F| = 17 \)
- \( |E| = 13 \)
...