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1. Let n be a positive integer. Classify the languages (i) R = {(M)IM is a TM and L(M) contains exactly n strings) (ii) S- (M)|M is a TM and L(M) contains more than n strings as (a) decidable, (b) Turing-recognizable but not co-Turing-recognizable, (c) co-Turing-recognizable but not Turing-recognizable, (d) neither Turing-recognizable nor co-Turing-recognizable. Justify your answers.
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Solution Answer: R -> Neither Turing-recognizable nor co-Turing-recognizable S -> Turing-recognizable Explanation S is Turing

At every phase, we execute single step of every active machines, and then create a new machine, and do again, thus interleavi

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