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

Question

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

Professor PC Thomas Classes · Answer

Consider functions from $X$ to $\{1,2,3,4\}$. $A=f^{-1}(\{1\}), B=f^{-1}(\{2\}), C=f^{-1}(\{3\})$