Computability and Decidability $(10$ points$)$

a$)$ What is the Turing machine halting problem? Is it decidable? Is the language that a Turing machine accepts a recursive language or recursively enumerable language?

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b$)$ Given an unrestricted grammar $G,$ it has been known that the problem of determining whether or not $L(G)=$ is undecidable. Let $M_1$ and $M_2$ be arbitrary Turing machines. Show that the problem $"L(M_1)subeL(M_2)"$ is undecidable.

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