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If $\mathrm{A}=\{x, y, z\}, \mathrm{B}=\{1,2\}$, then the total number of relations from set $\mathrm{A}$ to set $\mathrm{B}$ are
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It is given that $A=\{x, y, z\}$ and $B=\{1,2\} .$
$\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}$
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 $2^{6} .$
$\therefore A \times B=\{(x, 1),(x, 2),(y, 1),(y, 2),(z, 1),(z, 2)\}$
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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