Line 7: Line 7:
  
 
Union  is commutative <br/>
 
Union  is commutative <br/>
<math>A\cup B = b\cup A</math> <br/>
+
<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 09:10, 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} $


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