If $\mathrm{A}=\{x, y, z\}, \mathrm{B}=\{1,2\}$, then the total number of relations from set $\mathrm{A}$ to…

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
  1. 64
  2. 16
  3. 32
  4. 8

Solution

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 $2^{6} .$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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