I hope computing questions are fine here. I'm trying to show that for all binary numbers $A$ and $B$, $A+B - (A \cap B) = A \cup B$.
It's confusing me firstly because I'm not sure what the "set theoretical equivalent" of binary addition is.
I assumed this could be treated as a type of group theory problem, since binary numbers are sets of $1$'s and $0$'s, and the operations $\cap$ and $\cup$ are defined on those sets.
This would make sense if we interpret $A \cap B$ as the bitwise "and" ($\land$) (or intersection, if you look at sets interpretation), $A \cup B$ as the bitwise "or" ($\lor$) of the numbers (which is their union in the set interpretation).
E.g. $7 \cap 11 =$
0b0111$\land$0b1011$=$0b0011$= 3$, $7 \cup 11 =$0b0111$\lor$0b1011$=$0b1111$=15 $ , so we'd need $7 + 11 - 3 = 15$