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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

Statements 1, 3, and 4 are true. Statement 2 is false: Turing-recognizable (RE) languages are closed under union but NOT under complementation. So only statement 2 is false.

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