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Given the following statements: (i) Recursive enumerable sets are closed under complementation. (ii) Recursive sets are closed under complements. Which is/are the correct statements?

Given the following statements: (i) Recursive enumerable sets are closed under complementation. (ii) Recursive sets are closed under complements. Which is/are the correct statements? Correct Answer II only

Recursive languages are closed under the following operations. The Kleene star L * of L The concatenation L * o P of L and P The union L U P The intersection L ∩ P.

Related Questions

Assume statements S1 and S2 defined as: S1: L2-L1 is recursive enumerable where L1 and L2 are recursive and recursive enumerable respectively. S2: The set of all Turing machines is countable. Which of the following is true?
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
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.
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.
Consider the following statements in respect of sets: 1. The union over the intersection of sets is distributive. 2. The complement of the union of two sets is equal to the intersection of their complements. 3. If the difference between the two sets is equal to the empty set, then the two sets must be equal. Which of the above statements are correct?
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?
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 X be a recursive language and Y be a recursively enumerable but not recursive language. Let W and Z be two languages such that Y̅ reduces to W, and Z reduces to X̅ (reduction means the standard many-one reduction). Which one of the following statements is 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?
Choose the correct option: Statement: If L1 and L2 are recursively enumerable languages over S, then the following is/are recursively enumerable.