Which of the following statements is/are false? For every non-determin...
Given,
Statement (1): "For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine".
It is a true statement. A non-deterministic Turing machine can be simulated by a deterministic Turing machine with exponential time.
Statement (2): "Turing recognizable languages are closed under union and complementation".
Turing recognizable languages are "not" closed under complementation. For any Turing recognizable language, the turing machine "T' recognizing 'L', may not terminate on inputs x ∉ L.
So, this is false.
Statement (3): "Turing decidable languages are closed under intersection and complementation".
Turing decidable languages are closed under union and complementation. It is easy to construct a turning machine to decide L1 ∪ L2, L1 if L1, L2 are Turing decidable.
So, this is a true statement.
Statement (4): "Turing recognizable languages are closed under union and intersection".
It is a true statement.
Hence, the correct option is (C).