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3. 121 marks] Prove using reductions that the following languages are undecidable. (Do not use Rice's theorem as a black box!) OX (a) [5 marks]

3. 121 marks] Prove using reductions that the following languages are undecidable. (Do not use Rice's theorem as a black box!) OX (a) [5 marks] Show via a reduction from the halting problem that { M, w) | M is a TM which does not halt on input w } is undecidable

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