The fact that SL_{2} is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem
L_{1} ∩ L_{2 = }
We know that the intersection of SL_{2} languages is also SL_{2}. If the complement of SL_{2} languages was also necessarily SL_{2}, then _{} would be SL_{2} contradicting the fact that there are SL_{2} languages whose union are not SL_{2}.
Lemma The class of strictly 2-local languages is not closed under complement .