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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?

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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?

(a) I only

(b) II only

(c) Both I and II

(d) Neither I nor II

This question was addressed to me in homework.

My enquiry is from Context Free Grammar topic in section Contextfree Grammar and Syntax Analysis of Compiler

1 Answer

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Correct answer is (b) II only

The explanation is: 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.

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