Complement - operations on languages, Theory of Computation

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The fact that SL₂ is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem

L₁ ∩ L_{2 =}

We know that the intersection of SL₂ languages is also SL₂. If the complement of SL₂ languages was also necessarily SL₂, then would be SL₂ contradicting the fact that there are SL₂ languages whose union are not SL₂.

Lemma The class of strictly 2-local languages is not closed under complement .

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