Michael Sipser Edition 3 Exercise 5 Question 30 (Page No. 241)
in Theory of Computation
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Use Rice’s theorem, to prove the undecidability of each of the following languages.

  1. $INFINITE_{TM} = \{\langle M \rangle \mid \text{M is a TM and L(M) is an infinite language}\}$.
  2. $\{\langle M \rangle \mid  \text{M is a TM and }\:1011 \in L(M)\}$.
  3. $ ALL_{TM} = \{\langle M \rangle \mid \text{ M is a TM and}\: L(M) = Σ^{\ast} \}$.
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