### Functions Question 9

#### Question 9 - 2024 (30 Jan Shift 1)

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

## Show Answer

#### Answer (44)

#### Solution

$f: A \rightarrow P(A)$

$a \in f(a)$

That means ‘a’ will connect with subset which contain element ’ $a$ '

Total options for 1 will be $2^{6}$. (Because $2^{6}$ subsets contains 1 )

Similarly, for every other element

Hence, total is $2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6} \times 2^{6}=2^{42}$

Ans. $2+42=44$