If $L_{1}$ is a context free language and $L_{2}$ is a regular language which of the following is are false?

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Solution

(a) Since CFLs are closed under regular difference, so $L_{1} - L_{2} = C F L - r e g u l a r = C F L s$
So option (a) is false.
(b) Since context free language is closed under regular intersection so $L_{1} \cap L_{2} = C F L \cap R E G = C F L$
So option (b) is true.
(c) Context free language is not closed under complementation.So $\sim L_{1}$ is not context free language.So option (c) is flase.
(d) Regular language are closed under complementation.So $\sim L_{2}$ is regular.
So option (d) is true.

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