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For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true? I. L̅1 (complement of L1) is recursive II. L̅2 (complement of L2) is recursive III. L̅1 is context-free IV. L̅1 ∪ L2 is recursively enumerable
Let L1, L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT? I. L1 ∪ L2 is context-free II. L̅1 is context-free III. L1 – R is context-free IV. L1 ∩ L2 is context-free
Study the accompanying Venn diagram that represents groups of persons speaking five different languages as follows. Oblong circle = Marathi ; Rectangle = Kannada, Circle = English, Triangle = Gujarati, Equilateral quadrangle = Hindi Using above information select the false statement/s from following list. (a) Area c represent persons speaking 5 languages but area d represents persons speaking 4 languages only. (b) Areas b and d represent persons speaking same number of languages. (c) Areas f, b and e represent persons speaking same languages. (d) Areas g and h represent persons who speak two languages only. 
Consider the following languages L1 = {ap | p is a prime number} L2 = {anbmc2m | n ≥ 0, m ≥ 0} L3 = {anbnc2n | n ≥ 0} L4 = {anbn | n ≥ 1} Which of the following are CORRECT? I. L1 is context-free but not regular. II. L2 is not context-free III. L3 is not context-free but recursive. IV. L4 is deterministic context-free
Which of the following statement(s) is/are TRUE? (i) The family of context-free languages are the proper subset of the family of regular languages. (ii) The family of recursive languages is a proper subset of the family of recursively enumerable languages.
Which of the following problems are decidable? I. Checking whether two regular languages are equivalent languages II. Checking whether two non-deterministic finite automata accept the same language III. Checking whether two context free grammars generate equivalent languages  IV. Checking whether a language of a context free grammar is non-empty
United Nations has declared the year 2019 as 'Indigenous Languages Year'. The purpose is : (a) To protect the Indigenous Languages in the world. (b) To create consciousness about decaying Indigenous Languages. (c) Resurrection of declining these languages. (d) To realise the contribution of these languages to the world cultural diversity. Which of the above purpose/purposes is/are correct ?
Consider the following languages over the alphabet Σ = {0,1, c}: L1 = {0n1n | n ≥ 0} L2 = {wcwr | w ϵ {0,1}*} L3 = {wwr | w ϵ {0,1}*} Here, w­r is the reverse of the string w. Which of these languages are deterministic Context-free languages?
Which of following problems are undecidable? I. Membership problem in context-free languages II. Whether a given context-free language is regular III. Whether a finite state automation halts on all inputs IV. Membership problem for type 0 languages
Which of the following statements is /are correct in the context of The Jammu and Kashmir Official Languages Bill, 2020. 1. The Bill was for the inclusion of Kashmiri, Dogri and Hindi in the list of official languages in the Union Territory of Jammu and Kashmir. 2. The Bill is for the inclusion of Urdu and English in the list of official languages in the Union Territory of Jammu and Kashmir. Select the correct answer by using the code mentioned below.