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Which of the following statements is false?

1. Every NFA can be converted to an equivalent DFA
2. Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine
3. Every regular language is also a context-free language
4. Every subset of a recursively enumerable set is recursive

Correct answer: Every subset of a recursively enumerable set is recursive

Solution

This statement is false because while every recursively enumerable set can be recognized by a Turing machine, not all subsets of such sets are guaranteed to be recursive; some may be non-decidable.

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