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Prove the equality: $\bigcup$ and $\bigcap$
01-04-2011, 12:45 PM
Post: #1
Prove the equality: $\bigcup$ and $\bigcap$
Prove that
\[ \bigcup_{i \in I} \bigcap_{j \in J} A_{i,j}=\bigcap_{f \in J^I} \bigcup_{i \in I} A_{i,f(i)} \]
where $f \in J^I$ is a function such that $f:I \rightarrow J$.

http://www.artofproblemsolving.com/Forum...&p=2137628
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