Question $4.$ Design a Turing Machine to recognize language $L=\{\begin{array}{c}wcw\end{array}$ : where $\{$:$w\{a,b{\}}^{**}\}$ on $=\{a,b,c\},$ i$.$e$.,$ any $\{a,b,c{\}}^{**}$ string that can be divided in the middle by a $"c"$ and the left half consisting of only $"$a$"$ and $"$b$"$ is exactly same as the right half, e$.$g$.,$ aacaa, babcbab, aabcaab.

Question $5.$ Design a Turing Machine to compute $x-y$ for given positive integers $x$ and $y,$ where $x>y.$ Assume unary notation is used and there is a $0$ separating $x$ and $y.$ i$.$e$.,$

$q_{0}11$dots$1$ubrace$(1011.\mathrm{.}1$ubrace${)}_x$ubrace$(**ubrace)q_{f}11.\mathrm{.}1$