Use Rice’s theorem, to prove the undecidability of each of the following languages.
- $INFINITE_{TM} = \{\langle M \rangle \mid \text{M is a TM and L(M) is an infinite language}\}$.
- $\{\langle M \rangle \mid \text{M is a TM and }\:1011 \in L(M)\}$.
- $ ALL_{TM} = \{\langle M \rangle \mid \text{ M is a TM and}\: L(M) = Σ^{\ast} \}$.