(80pt) For each of the following languages, prove, without using Rice’s Theorem, whether it is (i) in D, (ii) in SD but not in D, or (iii) not in SD.
L1 = f<Mj f"; ab; ababg L(M)g
2 L2 = f<Mj L(M) \ (ab) is in niteg 3 L3 = f<Mj L(M) \ (ab) is niteg 4 L4 = f<Mj L(M) \ (ab) = ;g
5 L5 = f<Mj L(M) \ (ab) 6= ;g
6 L6 = f<Mj L(M) 6= L(M0) for any other TM M0g 7 L7 = f<M j :L(M) 2 Dg.
8 L8 = f<M j L(M) 2 SDg.
(20pt) For each of the languages in question 1, indicate whether Rice’s Theorem can be used or not to prove that the corresponding language is not in D. Explain why.
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