41 votes 41 votes Let $L_1, L_2$ be any two context-free languages and $R$ be any regular language. Then which of the following is/are CORRECT? $L_1 \cup L_2$ is context-free $\overline{L_1}$ is context-free $L_1 - R$ is context-free $L_1 \cap L_2$ is context-free I, II and IV only I and III only II and IV only I only Theory of Computation gatecse-2017-set2 theory-of-computation closure-property + – khushtak asked Feb 14, 2017 • retagged Jul 1, 2017 by Silpa khushtak 11.7k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply flash12 commented Jan 17, 2019 reply Follow Share Explain option iii please 1 votes 1 votes shashankrustagi commented Dec 1, 2020 reply Follow Share ERROR IN GO PDF THIRD OPTION – SIGN MISSING. 0 votes 0 votes tusharb commented Jul 20, 2022 reply Follow Share flash12 option iii) CFL-Regular 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 1) CFLs are closed under union. 2)CFLs are not enclosed under complementation and intersection. 3) L1−R = L1 intersection R' = L1 intersection R So CFL on intersection with Regular it will be CFL So Option B Suneel Padala answered Jan 30, 2019 Suneel Padala comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Only I and III are correct , so option B is correct. CFG are not closed under complement. and IV. CFG are not closed under intersection. Sanandan answered Oct 6, 2020 Sanandan comment Share Follow See all 0 reply Please log in or register to add a comment.