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| − | <math>A\cup B = | + | <math>A\cup B = B\cup A</math> <br/> |
| − | where <math>A</math> and <math>B</math> are | + | where <math>A</math> and <math>B</math> are sets. |
Latest revision as of 10:21, 1 October 2013
Theorem
Union is commutative
$ A\cup B = B\cup A $
where $ A $ and $ B $ are sets.
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} $
