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Jun 15, 2010 at 13:26 comment added KP Hart There's no need to credit anyone I think as it follows almost straight from the definitions. Maybe check this book (ams.org/mathscinet-getitem?mr=278261) to see if it isn't simply well known. (By the way, it suffices that $A\delta B$: either one of $A$ and $B$ meets both $X$ and $Y$ and we're done or $\lbrace A,B\rbrace=\lbrace X,Y\rbrace$, in which case we have $X\delta Y$ too.)
Jun 14, 2010 at 22:18 vote accept porton
Jun 14, 2010 at 22:13 comment added porton Thanks for your solution. In fact I solved myself, but my solution was less beautiful. KP Hart, do you want that I would refer to you in the article (about connectedness) which I am writing?
Jun 14, 2010 at 21:49 history answered KP Hart CC BY-SA 2.5