For all sets X and Y , Y ∩ (X-Y) ≠ Ø

Ok so I'll assume for all sets X and Y , Y ∩ (X-Y) = Ø

If I say Let set Y be the set of Integers and also let set X then

if Y = {1,2,3} and X = {4,5,6}

then Y ∩ (X-Y) = Ø because Ø is a subset of all sets ..including integers

subbing the Y value into the original leaves {1,2,3} ∩ ({4,5,6}-{1,2,3}) ≠ Ø

I think I have totally stuffed this but I tried.....

Any help would be appreciated..