Let \(S\) be a sample space, let \(A,\, B\subseteq S\) be events, and define a new set

\[ A-B = \{x\in S:x\in A\text{ and }x\notin B\}. \]

1. Draw a well-labeled picture of \(A\), \(B\), \(S\), and the set \(A-B\);
2. Write down an equivalent expression for \(A-B\) that only makes use of our three basic operations: union, intersection, and complement;
3. Prove that \(P(A-B)=P(A)-P(A\cap B)\).