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Definition (Unions And Intersections Of Finitely Many Sets)
Let $n$ be a natural number and suppose that $A_i$ is a set for each $ i\in \{1, 2,\ldots n \} $.
- The union of $A_1, A_2, \ldots, A_n$ is the set $$\bigcup_{i=1}^n A_i = \{x\mid x\in A_i \text{ for some } i\in\{1,2,\ldots,n\} \}.$$
- The intersection of $A_1, A_2, \ldots, A_n$ is the set $$\bigcap_{i=1}^n A_i = \{x\mid x\in A_i \text{ for all } i\in\{1,2,\ldots,n\} \}.$$