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Which of the following statements is FALSE?

  1. Recursive Enumerable Languages are not closed under set difference and complementation.
  2. Complement of context-free language must be recursive.
  3. If a problem $X$ is NP complete and $X \in P,$ then $NP = P$.
  4. Membership problem is not decidable for Recursive Languages.

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Membership problem is decidable under recursive languages. Turing machine for recursive language will either accept the given input string or it will reject the input string, so statement is false.
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