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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
Choose the correct option: Statement: If L1 and L2 are recursively enumerable languages over S, then the following is/are recursively enumerable.
Which of the following statement(s) is/are FALSE? (i) There exists a recursively enumerable language whose complement is not recursively enumerable. (ii) If a language L is recursive, then its complement is NOT recursive.
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.
Consider the following sets: S1. Set of all recursively enumerable languages over the alphabet {0,1} S2. Set of all syntactically valid C programs S3. Set of all languages over the alphabet {0,1} S4. Set of all non-regular languages over the alphabet {0,1} Which of the above sets are uncountable?
The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. If the maximum number of valves that can be closed at the same time are closed which of the following must true?
Which of the following statements is/are FALSE? 1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. 2. Turing recognizable languages are closed under union and complementation. 3. Turing decidable languages are closed under intersection and complementation. 4. Turing recognizable languages are closed under union and intersection.
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. 
The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. If R is closed and U is open, which of the following must be true?
Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?