3 votes 3 votes Given the following statements: A class of languages that is closed under union and complementation has to be closed under intersection A class of languages that is closed under union and intersection has to be closed under complementation Which of the following options is correct? Both (i) and (ii) are false Both (i) and (ii) are true (i) is true, (ii) is false (i) is false, (ii) is true Theory of Computation ugcnetcse-jan2017-paper3 theory-of-computation regular-language + – go_editor asked Mar 24, 2020 • edited Jan 30 by makhdoom ghaya go_editor 2.6k views answer comment Share Follow See 1 comment See all 1 1 comment reply Sanjay Sharma commented May 14, 2020 reply Follow Share A intersection B = (A'UB')' . since set is closed under complement and union so it must be closed under intersection so a is true ( union and complement-> intersection no such relation between union , intersection --> complementation 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes Based on the above closure properties, (A) is TRUE. Because Regular Languages are an example of being closed under union and complementation, and thus under intersection. (B) is FALSE. Because Recursively Enumerable Languages are closed under both union and intersection but NOT under complementation. aiyyar.aarushi answered Nov 17, 2018 aiyyar.aarushi comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Here we can derive this statement with the help of closure properties S1: true as it is the case for Regular grammar S2:false, as in RE language it is closed under Union,Intersection but not in complementation' so 3 is correct answer here Aboveallplayer answered Jan 28, 2017 Aboveallplayer comment Share Follow See 1 comment See all 1 1 comment reply Sanjay Sharma commented Sep 26, 2018 reply Follow Share just by taking exmaple of regular we can't conclude S1 is true , we need to check for CSL and REC too 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes https://gateoverflow.in/113790/ugcnet-dec2016-iii-21 ANS: C mohitbawankar answered Oct 9, 2017 mohitbawankar comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Here we can derive this statement with the help of closure properties S1: true as it is the case for Regular grammar S2:false, as in RE language it is closed under Union,Intersection but not in complementation' so 3 is correct answer here Aboveallplayer answered Jan 31, 2017 Aboveallplayer comment Share Follow See all 0 reply Please log in or register to add a comment.