Q14

The aim of the following question is to prove that the language $\{M \mid M$ $\text {is the code of the Turing Machine which, irrespective of the input, halts and outputs a}$ $1\}$, is undecidable. This is to be done by reducing from the language $\{M', x \mid M'$ $\text{ halts on }$ $x\}$, which is known to be undecidable. In parts (a) and (b) describe the $2$ main steps in the construction of $M$. In part (c) describe the key property which relates the behaviour of $M$ on its input w to the behaviour of $M'$ on $x$.