# Thread: Basic proof

1. ## Basic proof

I need to prove that $A-B = A - (A\cap B)$

Using a Venn diagram, this proof is so trivial but how do I prove this mathematically?

So far I have
$A-B = A\cap B^{C}$
$=A\cap(S-B)$ where S is the sample space

But now I'm stuck...

2. Hi

You can prove it with two inclusions. One is quite simple:

$A-B\subseteq A-(A\cap B)\ .$ Do you see why?

Then take $x\in A-(A\cap B)$. What does it mean for x?