| Line 7: | Line 7: | ||
Union is commutative <br/> | Union is commutative <br/> | ||
| − | <math>A\cup B = | + | <math>A\cup B = B\cup A</math> <br/> |
where <math>A</math> and <math>B</math> are events in a probability space. | where <math>A</math> and <math>B</math> are events in a probability space. | ||
Revision as of 08:10, 29 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} $
