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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.

1. 1 and 4 only
2. 1 and 3 only
3. 2 only
4. 3 only

Correct answer: 2 only

Solution

Statement 2 is false because Turing recognizable languages are not closed under complementation; while they are closed under union, the complement of a recognizable language may not be recognizable.

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