Question

If n(A) = 2, n(B)=3, then find the number of relation from A to B .​

Answer 1

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

$\mathsf{n(A)=2\;and\;n(B)=3}$

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

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

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

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

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

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

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

$\mathsf{=2^{n(A\,X\,B)}}$

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

$\mathsf{=2^{2\,\times\,3}}$

$\mathsf{=2^{6}}$

$\mathsf{=64}$

$\therefore\textbf{The number of relations from A to B is 64}$

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

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

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