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You might notice that the symbols for union and intersection slightly resemble the logic symbols for “or” and “and.” This is no accident. What does it mean for \(x\) to be an element of \(A\cup B\text{?}\) It means that \(x\) is an element of \(A\) or \(x\) is an element of \(B\) (or both). That is,

\begin{equation*} x \in A \cup B \qquad \Iff \qquad x \in A \vee x \in B\text{.} \end{equation*}
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