Write down the expression in set notation corresponding to each of the following events:

1. the event occurs if exactly one of the the events \(A\) and \(B\) occurs.
2. the event which occurs if none of the events \(A\), \(B\), or \(C\) occurs.
3. the event which occurs if exactly one of the events \(A\), \(B\), or \(C\) occurs.
4. the event which occurs if exactly two of the events \(A\), \(B\), or \(C\) occurs.
5. the event which occurs if exactly three of the events \(A\), \(B\), or \(C\) occurs.

(From [Pitman p.30, #2] )