Let A = {1, 2, 3, ..., 7} and let P(A) denote the power set of A. If the number of functions f : A ? P ( A ) such that a ? f ( a ) , ? a ? A is m n , m and n ? N and m is least, then m + n is equal to _____. [2024]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let A = {1, 2, 3, ..., 7} and let P(A) denote the power set of A. If the number of functions $f : A \to P (A)$ 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 _____. [2024]

Ans.
(44)

Given, $f : A \to P (A) \Rightarrow a \in f (a)$

It means $' a'$ will connect with subset which contain element $a .$

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

Similarly, for every other element

Now, number of functions from A to P(A) = ${(2^{6})}^{7} = 2^{42}$

i.e., $m + n = 2 + 42 = 44$

Want Us to Email you About Special Offers & Updates?