Here are two definitions of languages that are similar to the definition of $L_{d}$, yet different from that language. For each, show that the language is not accepted by a Turing machine, using a diagonalization-type argument. Note that you cannot develop an argument based on the diagonal itself, but must find another infinite sequence of points in the matrix suggested by Fig.$9.1$.
- The set of all $w_{i}$ such that $w_{i}$ is not accepted by $M_{2i}$.
- The set of all $w_{i}$ such that $w_{2i}$ is not accepted by $M_{i}$.