Hello, this is a problem from Munkres: Let X and Y be conected spaces such that $\displaystyle Y\subset X$. If A and B are a separation of X-Y prove that $\displaystyle Y\cup A\,and\,Y\cup B$ are conected.

I can only prove that $\displaystyle Y\cup A\,or\,Y\cup B$ is conected and since I've read from a Spanish transation I wonder whether the problem is correctly formulated.