Let (N; v) and (N; w) be two coalitional games with the same set of players.
Let x ∈ X(B; v) and y ∈ X(B; w). Does x + y ∈ X(B; v + w) necessarily hold? Does x - y ∈ X(B; v - w) necessarily hold?
If you answer yes to either question, provide a proof. If you answer no, present a counterexample.