Question

If there are 512 relations from a set A= 2,3,5 to a setB, then the number of elements in B is​

Answer 1

Given : There are 512  relations from set A to B.

set A = { 2 , 3 , 5}

To Find :  how many the number of elements in the set B​

Solution:

512 relations from set A to B.

set A = { 2 , 3 , 5}

n(A) = 3

Relation from set A to B.  =  $2^{n(A).n(B)}$

Relation from set A to B = 512  = 2⁹

Equating Both

=> n(A) * n(B) =9

n(A) = 3

=> 3 * n(B) = 9

=> n(B) = 3

number of elements in the set B​  = 3

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Answer 2

$\underline{\textbf{Given:}}$

$\mathsf{A=\{2,3,5\}\;and\;}$

$\textsf{The number of relations from A to B is 512}$

$\underline{\textbf{To find:}}$

$\textsf{The number of elements in B}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Relaton:}}$

$\textsf{Let A and B be two subsets. A relation from A to}$

$\textsf{B is a subset of A X B}$

$\textsf{No.of relations from A to B = No. of subsets of A X B}$

$\implies\mathsf{512=2^{n(A{\times}B)}}$

$\implies\mathsf{2^9=2^{n(A{\times}B)}}$

$\implies\mathsf{n(A{\times}B)=9}$

$\implies\mathsf{n(A){\times}n(B)=9}$

$\implies\mathsf{3{\times}n(B)=9}$

$\implies\mathsf{n(B)=\dfrac{9}{3}}$

$\implies\boxed{\mathsf{n(B)=3}}$

$\underline{\textbf{Find more:}}$