# Talk:Set Difference with Intersection

Why isn't the following even up:

$X \setminus \left({Y \cap Z}\right) = \left({X \setminus Y}\right) \cup \left({X \setminus Z}\right)$

Also, note:

$X \setminus \left({Y \cap Z}\right) = \left({X \setminus Y}\right) \cup \left({Y \setminus Z}\right)$

might be valuable as a corollary of the above (which I need on Union of Symmetric Differences).

Now, where to put them? --Lord_Farin 06:35, 24 March 2012 (EDT)

Try De Morgan's Laws (Set Theory)/Set Difference/Difference with Intersection. --prime mover 06:57, 24 March 2012 (EDT)

Sorry. FFR, I have added an also see to there. --Lord_Farin 07:03, 24 March 2012 (EDT)

As there is no obvious name for $X \setminus \left({Y \cap Z}\right) = \left({X \setminus Y}\right) \cup \left({Y \setminus Z}\right)$, suggest then that it go in as De Morgan's Laws (Set Theory)/Set Difference/Difference with Intersection/Corollary and take it from there. --prime mover 07:06, 24 March 2012 (EDT)
Just did that. --Lord_Farin 07:16, 24 March 2012 (EDT)