Can someone please help with the proof of this? Given an unambiguous context-free language L and an unambiguous regular language L (moreover, every regular language is unambiguous) such that L∩ R = ∅, then prove that L∪ R is also unambiguous.
Take unambiguous grammars for L and R with start symbols $S_L$ and $S_R$. For L union R take a grammar that starts with $S-&gt;S_L$, $S-&gt;S_R$. Since no string is both in L and R, only one of the initial two rules can succeed, so the grammar is unambiguous.