The number of elements in $\{(\mathrm{A}, \mathrm{B}): \mathrm{A}, \mathrm{B} \subset \mathrm{X}, \m

Question

The number of elements in $\{(\mathrm{A}, \mathrm{B}): \mathrm{A}, \mathrm{B} \subset \mathrm{X}, \mathrm{A} \cap \mathrm{B}=\phi, \mathrm{A} \cup \mathrm{B}=\mathrm{X}\}$ is

Professor PC Thomas Classes · Answer

If $\mathrm{f}: \mathrm{X} \rightarrow\{1,2\}, \mathrm{A}=\mathrm{f}^{-1}(\{1\})$ and $\mathrm{B}=\mathrm{f}^{-1}(\{2\})$ then $\mathrm{A} \cap \mathrm{B}=\phi$ and $\mathrm{A} \cup \mathrm{B}=\mathrm{X}$