Results Concerning Set Difference with Intersection

Theorem
Let:
 * $S \setminus T$ denote set difference
 * $S \cap T$ denote set intersection.

Also see

 * De Morgan's Laws :Difference with Intersection, in which:


 * $R \setminus \left({S \cap T}\right) = \left({R \setminus S}\right) \cup \left({R \setminus T}\right)$

shows that set difference is not left distributive over set intersection.