EDB — 23W

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E54

[23W]The notation in [026] differs from the usual one, which is \(⋃_{i∈ I}C_ i\), where \(I\) is a non-empty family of indices and \(C_ i\) are sets; as seen in [1Y2].

How can you define \(⋃_{i∈ I}C_ i\) using the axiom of union presented [026]? (Sugg. re-read the note [01M])

Eventually you should obtain

\begin{equation} \forall x, x\in ⋃_{i∈ I}C_ i \iff ∃ i∈ I, x\in C_ i\quad . \label{eq:unione_ simpl_ in_ logica} \end{equation}
55

Solution 1

[027]

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