Question: Let $ONE - OR - ALL ( L _ 1 , L _ 2 , L _ 3 ) $ be the set which contains

Let $ONE-OR-ALL(L_1, L_2, L_3)$ be the set which contains all strings which are either members of all three languages $L_1, L_2, L_3$ or are contained in \emph{exactly} one of the three languages. Show that, if $L_1, L_2$, and $L_3$ are regular, then $ONE-OR-ALL(L_1, L_2, L_3)$ is also regular.

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