Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$
Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$
We have,
$A \times B=\{(1,3),(1,4),(2,3),(2,4)\}$
Since $n( A \times B )=4,$ the number of subsets of $A \times B$ is $2^{4} .$
Therefore, the number of relations from $A$ into $B$ will be $2^{4}$.
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