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!

Notice that $A\setminus B=A\cap B^c$ and we have $A=A\cap(B\cup B^c)=(A\cap B)\cup(A\cap B^c)$ and the sets in the last union are disjoint so
$$|A|=|A\cap B|+|A\cap B^c|$$
and we can conclude.
