A) Total students = 75, n(P H) = 75, n(P H) = 10, n(P) : n(H) = 2 : 3. Find n(P) and n(H).

10. a)
Given:
Total students = 75
Students who like picnic (P) or hiking (H) or both, $n(P \cup H) = 75$.
Students who like both activities, $n(P \cap H) = 10$.
The ratio of the number of students who like picnic to those who like hiking is $n(P) : n(H) = 2 : 3$.

Step 1: Find the values of $n(P)$ and $n(H)$.
We know the formula for the union of two sets: $n(P \cup H) = n(P) + n(H) - n(P