Michael Sipser Edition 3 Exercise 5 Question 30 (Page No. 241)

Question

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} \}$.