Let \(A\), \(B\), and \(C\) be three arbitrary events, and let \(D\) denote the event that “exactly one of these three events occurs.”

1. Draw a cartoon of \(A\), \(B\), \(C\), and \(D\);
2. Use the three basic set operations (union, intersection, and complement) to express \(D\) in terms of \(A\), \(B\), and \(C\);
3. Show that

\[ P(D)=P(A) + P(B) + P(C) - 2P(A \cap B) - 2P(A \cap C) - 2P(B \cap C) + 3P(A \cap B \cap C). \]