(New page: == Theorem == Union is commutative <br/> <math>A\cup B = b\cup A</math> <br/> where <math>A</math> and <math>B</math> are events in a probability space. ---- ==Proof== <math>\begin{a...) |
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Revision as of 20:49, 28 September 2013
Theorem
Union is commutative
$ A\cup B = b\cup A $
where $ A $ and $ B $ are events in a probability space.
Proof
$ \begin{align} A\cup B &\triangleq \{x\in\mathcal S:\;x\in A\;\mbox{or}\; x\in B\}\\ &= \{x\in\mathcal S:\;x\in B\;\mbox{or}\; x\in A\}\\ &= B\cup A\\ \blacksquare \end{align} $
