it's gonna be true again if it's not two symbols at the bottom you only have one we just a bit more okay so at the bottom there is always gonna be two leaves at that lowest branch then without loss of generality we can assume that symbols x and y have the same parent does I have to meet a kids just bill imagine your tree looks like this it can be an X's here y is here and there's a Z here and a W here could be it they don't have the same parent but because they're the lowest probability symbols they will always sit at the lowest lowest level