Question

Let A = {1, 2} and B = {3, 4}. Find the total number of relations from A into B.

Answer 1

We have,

A = {1, 2} and B = {3, 4}

$\therefore n\left(A\right)=2andn\left(B\right)=2$

$\Rightarrow n\left(A\right)\times n\left(B\right)=2\times 2=4$

$\Rightarrow n(A\times B)=4$

$[\because n(A\times B)=n(A)\times n(B\left)\right]$

So, there are $2^4=16$ relations from A to B.

$\left[\begin{array}{c}\because n\left(x\right)=a,n\left(y\right)=b\\ \Rightarrow \text{Total number of relations}=2^{ab}\end{array}\right]$