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Notice that the shaded regions above could also be arrived at in another way. We could have started with all of \(C\text{,}\) then excluded the region where \(C\) and \(A\) overlap outside of \(B\text{.}\) That region is \((A \cap C) \cap \bar B\text{.}\) So the above Venn diagram also represents \(C \cap \bar{\left((A\cap C)\cap \bar B\right)}\text{.}\) So using just the picture, we have determined that

\begin{equation*} (B \cap C) \cup (C \cap \bar A) = C \cap \bar{\left((A\cap C)\cap \bar B\right)}\text{.} \end{equation*}
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