Problem Statement: Let Y be a subset of X, and X and Y are connected, show that if A and B form a seperation of X-Y then YUA and YUB are connected. Attempt at solution: Well I'm not sure where the fact that X is connected comes to play (perhaps it gurantees us the possibility of X-Y not to be connected). anyway if we look at: seperations of YUB=CUD and YUA=C'UD' then Y=(YUB)-B=(C-B)U(D-B), Y=(YUA)-A=(C'-A)U(D'-A) which are both seperations of Y which is a contradiction to Y being connected, am I correct here or yet again wrong? any input? thanks in advance.