13 votes 13 votes State whether the following statements are TRUE or FALSE: All subsets of regular sets are regular. Theory of Computation gate1987 theory-of-computation regular-language true-false + – makhdoom ghaya asked Nov 9, 2016 • recategorized Apr 22, 2021 by Lakshman Bhaiya makhdoom ghaya 2.5k views answer comment Share Follow See 1 comment See all 1 1 comment reply raja11sep commented Jul 15, 2021 reply Follow Share Every finite subset of a non-regular set is regular. Every finite subset of a regular set is regular. 0 votes 0 votes Please log in or register to add a comment.
Best answer 25 votes 25 votes False! $a^*b^*$ is regular but its subset $a^nb^n$ is not regular. Anusha Motamarri answered Nov 9, 2016 • edited Apr 14, 2021 by Lakshman Bhaiya Anusha Motamarri comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments vishalshrm539 commented Dec 22, 2017 reply Follow Share yes. 0 votes 0 votes Sumaiya23 commented Jan 4, 2018 reply Follow Share Finite subsets of regular sets are regular. 10 votes 10 votes raja11sep commented Jul 15, 2021 reply Follow Share Finite subsets of regular sets are regular. Sumaiya23 A finite subset of any non regular set is also regular, right !. As every finite set is regular. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes $\sum ^{*}$ is regular which contains every language such as a $a^{n}b^{n}$ which is non regular. Therefore, Regular Languages are not closed under subset. Harish Hatmode answered Nov 3, 2023 Harish Hatmode comment Share Follow See all 0 reply Please log in or register to add a comment.