For sets $A,B,C$, $(A\setminus B)\subset (A\setminus C)\cup (C\setminus B)$ First of all, I am sorry for my bad english, I am from Brazil :-) I have problem with proof for some set theory task.
Here it is:

$A,B,C$ are three sets. Show that:
$$(A\setminus B) \subset (A\setminus C) \cup (C\setminus B)$$

It is clear by looking at diagrams but I do not know how I show! It is not too hard I think...
Thank you for the help,
Igor

If you take out from $A$ things that are in $B$, what is left is certainly things in $A$ not in $C$, except for things in $C$ that were not in $B$, so if you add the latter you are all set. The formula is nothing more than this.
