Which of the following statements is not correct ?

This question was previously asked in
UGC NET Computer Science (Paper 3) Nov 2017 Official Paper
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  1. Every recursive language is recursively enumerable.
  2. L  = {0n 1n 0n | n = 1, 2, 3, ....} is recursively enumerable.
  3. Recursive languages are closed under intersection
  4. Recursive languages are not closed under intersection

Answer (Detailed Solution Below)

Option 4 : Recursive languages are not closed under intersection
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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The correct answer is "option 4".

EXPLANATION

option1: Correct

If there exists a Turing machine that accepts every string of the language and does not accept any string that is not in the language then, the language is recursively enumerable language.

So, every recursive language is also recursively enumerable.

option2: Correct

The language L  = {0n 1n 0n | n = 1, 2, 3, ....} is recursive enumerable and it is accepted by Linear bounded Automataon.

option3: Correct

Recursive languages are closed under intersection.

option4: Not Correct

Since recursive languages are closed under intersection.

Hence, the correct answer is "option 4".

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