The maximum number of sets which can be obtained from two given nonempty sets A and B , different fr

Question

The maximum number of sets which can be obtained from two given nonempty sets A and B , different from $A$ and $B$ using only the union and difference operations of sets, is

Professor PC Thomas Classes · Answer

The sets which can be obtained are $A \cup B$,  \ $ \begin{aligned} & \mathrm{A}-\mathrm{A}, \mathrm{~A}-\mathrm{B}, \mathrm{~B}-\mathrm{A},(\mathrm{~A}-\mathrm{B}) \cup(\mathrm{B}-\mathrm{A}) \ & \mathrm{A}-(\mathrm{A}-\mathrm{B})=\mathrm{A} \cap \mathrm{~B} \end{aligned} $