Question:
Let $A=\{x, y, z\}$ and $B=\{1,2\}$. Find the number of relations from $A$ to $B$.
Solution:
It is given that $A=\{x, y, z\}$ and $B=\{1,2\}$.
$\therefore \mathrm{A} \times \mathrm{B}=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}$
Since $n(A \times B)=6$, the number of subsets of $A \times B$ is $2^{6}$.
Therefore, the number of relations from $A$ to $B$ is $2^{6}$.
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