$A \cup B \equiv C $ then what is $A$ in terms of $B,C$?
I tried to use $A\cup B \equiv (A-B)\cup(A \cap B)\cup(B-A) $ to find a similar expression for $A \cap B$ but got nowhere.
From the elementary set theory that I did 40 or so years ago I don't recall any material on inverse of set theory operations i.e. union, intersection, complement, difference.
Complement is easy as it is it's own inverse $(A^C)^C=A$
not sure if inverse of difference operator is unique, for example, one can use $(A-B)\cup A \equiv A$ to construct one inverse of difference $ -X$.
when doing algebra, inverse operations are the first tricks to learn, but was the topic of inverse operations of set theory ever mentioned?