(a) Construct a register machine to compute the function $f(m, n):=m+n$. State the relationship between partial recursive functions and partial computable functions. Show that the function $g(m, n):=m n$ is partial recursive.

(b) State Rice's theorem. Show that the set $A:=\left\{n \in \mathbb{N}|| W_{n} \mid>7\right\}$ is recursively enumerable but not recursive.