(New page: Category:ECE600 Category:Set Theory Category:Math == Theorem == Intersection is commutative <br/> <math>A\cap B = B\cap A</math> <br/> where <math>A</math> and <math>B</mat...) |
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Intersection is commutative <br/> | Intersection is commutative <br/> | ||
<math>A\cap B = B\cap A</math> <br/> | <math>A\cap B = B\cap 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 11:21, 1 October 2013
Theorem
Intersection is commutative
$ A\cap B = B\cap A $
where $ A $ and $ B $ are sets.
Proof
$ \begin{align} A\cap B &\triangleq \{x\in\mathcal S:\;x\in A\;\mbox{and}\; x\in B\}\\ &= \{x\in\mathcal S:\;x\in B\;\mbox{and}\; x\in A\}\\ &= B\cap A\\ \blacksquare \end{align} $
