For finite sets M and N and P, if the cross product of M and N is equal to the cross product of M and P, then N = P. (if MxN=MxP then N=P)
my prof told us its FALSE. but why?
in ordinary language, if we never pick a first coordinate, it doesn't matter which second coordinate we were going to pick, it never gets chosen.
the same logic goes for the second coordinate: no matter which first coordinate we pick, if we never choose the second coordinate, we never get a pair.
picking an element of the empty set pretty much stops us dead in our tracks, it has no elements to pick.