Probability with Measure
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1.6 Exercises
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1.1 Give a careful proof by induction of the fact that if \(\bf B\) is a Boolean algebra and \(A_{1}, A_{2}, \ldots , A_{n} \in {\bf B}\), then \(A_{1} \cup A_{2} \cup \cdots \cup A_{n} \in {\bf B}\).
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1.2 Show that if \(S\) is a set containing \(n\) elements, then the power set \({\cal P}(S)\) contains \(2^{n}\) elements.
Hint: How many subsets are there of size \(r\), for a fixed \(1 \leq r \leq n\)? The binomial theorem may also be of some use.
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1.3 OMITTED