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!

Direct Proof:
Suppose $|A| = x.$
Suppose $|A∩B|= y: y < x.$
Then, $x - y$ denotes the cardinality of all elements in $A$ and not $B$.
$A\backslash B$ is the set containing all elements in $A$ and not $B$.
Thus, $|A\backslash B|= x - y = |A|−|A∩B|$.
