Definition
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[1W1] Given \(I\) a non-empty family of indexes and given \(C_ i\) sets (one for each \(iβ I\)), we define the intersection
\[ β_{iβ I}C_ i \]
which is the set that contains the elements that belong to all sets \(C_ i\) (for all \(iβ I\)).
If only two sets are given \(C_ 1,C_ 2\), we usually write \(C_ 1β© C_ 2\) to indicate the intersection, and you have
\[ C_ 1β© C_ 2 {\stackrel{.}{=}}\left\{ x β C_ 1βͺ C_ 2 : xβ C_ 1 β§ xβ C_ 2 \right\} \quad ; \]