(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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| + | [[Category:ECE600]] | ||
| + | [[Category:Set Theory]] | ||
| + | [[Category:Math]] | ||
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== Theorem == | == Theorem == | ||
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 | + | where <math>A</math> and <math>B</math> are sets. |
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\blacksquare | \blacksquare | ||
\end{align}</math> | \end{align}</math> | ||
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| + | ---- | ||
| + | [[Proofs_mhossain|Back to list of all proofs]] | ||
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} $
