Cardinality of Sets Proof I have a question as such:

Let $|A|$ denote the number of elements in A. For finite sets $A,B$,
  prove that $|A\backslash B| = |A| - |A\cap B|$, where $\backslash$
  stands for set difference.

Could someone show me how to prove it, please? I'm having difficulty working out a proof that feels rigorous enough - it seems too obvious!

HINT:
Recall that for disjoint sets $X,Y$ we have that $|X\cup Y|=|X|+|Y|$. Take $X=A\setminus B$ and $Y=A\cap B$, observe that they are indeed disjoint, and simplify the equation.
