I already know simillar form of $\#A+\#B=\#(A\cup B) + \#(A\cap B)$ holds with finite dimensional $F$-vector spaces(not clear with infinite dimensional) like this form...
$$ \dim V+\dim W=\dim(V+W)+\dim(V\cap W) $$
which is corollaty of Second Isomorphism Theorem.
I'm curious about this form... Are there exists simillar form or fomulae at any other parts?(such as group theory... or etc.)
