QUESTION #21 Set Operations

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is

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QUESTION #24 Types of Functions

Let A = \1, 2, 3, dots, 7\$A = \{1, 2, 3, \dots, 7\}$ and let P(A)$P(A)$ denote the power set of A$A$. If the number of functions f: A to P(A)$f: A \to P(A)$ such that a in f(a)$a \in f(a)$ forall a in A$\forall a \in A$ is m^n$m^n$, m$m$ and n in mathbbN$n \in \mathbb{N}$ and m$m$ is least, then m + n$m + n$ is equal to

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