Question

what is A ringsum B?

Answer 1

I guess you are talking about Boolean rings. In this context we usually define "multiplication" as the logical and operator and "sum" as the exclusive-or operator,\[xy \doteq x \land y\]\[x + y \doteq \left(x \lor y\right) \land \lnot\left(x \land y\right).\]where x and y are either true or false. This way the structure satisfies the axioms of ring theory, which is why it's called a Boolean ring. Therefore, A ring sum B is \[\left(A \lor B\right) \land \lnot\left(A \land B\right).\]

Answer 2

ok......yes i thnk i got my answer because what i know about A ringsum B is:
it includes A & B but nthng common from A & B.