Given a TM, T 1 , and any string w, there is clearly a TM, T 2

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Given a TM, T1, and any string w, there is clearly a TM, T2, that first screens its input to see whether it is the particular string w; if it is not the input is accepted, if it is w, then T1 is run on the input w. Pictorially,

Show that there is no decision procedure to determine whether any given TM (say T2) accepts all strings or not.

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