A Turing Machine for the language $\mathrm{L}=\left\{\mathrm{a}^{\mathrm{n}} \mathrm{b}^{\mathrm{m}} \mathrm{c}^{\mathrm{n}} \mathrm{d}^{\mathrm{m}} \mid \mathrm{n} \geq 1, \mathrm{~m} \geq 1\right\}$ is designed. The resultant model is $\mathrm{M}=$ $\left(\left\{\mathrm{q}_{0}, \mathrm{q}_{1}, \mathrm{q}_{2}, \mathrm{q}_{3}, \mathrm{q}_{4}, \mathrm{q}_{5}, \mathrm{q}_{6}, \mathrm{q}_{7}, \mathrm{q}_{\mathrm{f}}\right\},\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\},\left\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{X}_{1}, \mathrm{X}_{2}, \mathrm{Y}_{1}, \mathrm{Y}_{2}\right\}, \delta, \mathrm{q}_{0}, \mathrm{~B},\left\{\mathrm{q}_{\mathrm{f}}\right\}\right)$ and part of ' $\delta$ ' is given in the transition table. You need to write the following questions based on design of Turing Machine for the given language. Note that, while designing the Turing Machine $\mathrm{X}_{1}$ and $\mathrm{X}_{2}$ are used to work with 'a's and 'c's and $\mathrm{Y}_{1}$ and $\mathrm{Y}_{2}$ are used to handle 'b's and 'd's of the given string.
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline & \mathrm{a} & \mathrm{b} & \mathrm{c} & \mathrm{d} & \mathrm{X}_{1} & \mathrm{X}_{2} & \mathrm{Y}_{1} & \mathrm{Y}_{2} & \mathrm{~B} \\
\hline \mathrm{q}_{0} & \left(\mathrm{q}_{1}, \mathrm{X}_{1}, \mathrm{R}\right) & & & & \mathrm{M} 2 & & & & \\
\hline \mathrm{q}_{1} & \left(\mathrm{q}_{1}, \mathrm{a}, \mathrm{R}\right) & \left(\mathrm{q}_{1}, \mathrm{~b}, \mathrm{R}\right) & \mathrm{M} 1 & & & \left(\mathrm{q}_{1}, \mathrm{X}_{2}, \mathrm{R}\right) & & & \\
\hline \mathrm{q}_{2} & \left(\mathrm{q}_{2}, \mathrm{a}, \mathrm{L}\right) & \left(\mathrm{q}_{2}, \mathrm{~b}, \mathrm{~L}\right) & & & \left(\mathrm{q}_{2}, \mathrm{X}_{1}, \mathrm{R}\right) & \left(\mathrm{q}_{2}, \mathrm{X}_{2}, \mathrm{~L}\right) & & & \\
\hline \mathrm{q}_{3} & \mathrm{M} 3 & \left(\mathrm{q}_{4}, \mathrm{Y}_{1}, \mathrm{R}\right) & & & & \left(\mathrm{q}_{6} \mathrm{X}_{2}, \mathrm{R}\right) & & & \\
\hline \mathrm{q}_{4} & & \left(\mathrm{q}_{4}, \mathrm{~b}, \mathrm{R}\right) & & \left(\mathrm{q}_{5}, \mathrm{Y}_{2}, \mathrm{~L}\right) & & \mathrm{M} 5 & & \left(\mathrm{q}_{4}, \mathrm{Y}_{2}, \mathrm{R}\right) & \\
\hline \mathrm{q}_{5} & & \left(\mathrm{q}_{5}, \mathrm{~b}, \mathrm{~L}\right) & & & & \left(\mathrm{q}_{5}, \mathrm{X}_{2}, \mathrm{~L}\right) & \mathrm{M} 4 & \left(\mathrm{q}_{5}, \mathrm{Y}_{2}, \mathrm{~L}\right) & \\
\hline \mathrm{q}_{6} & & & & & & \left(\mathrm{q}_{6}, \mathrm{X}_{2}, \mathrm{R}\right) & & \left(\mathrm{q}_{7}, \mathrm{Y}_{2}, \mathrm{R}\right) & \\
\hline \mathrm{q}_{7} & & & & & & & & \left(\mathrm{q}_{7}, \mathrm{Y}_{2}, \mathrm{R}\right) & \left(\mathrm{q}_{6}, \mathrm{~B}, \mathrm{R}\right) \\
\hline
\end{array}
What is the Move in the cell with number $\text{'M3'}$ of the resultant Table?
- $\left(\mathrm{q}_{1}, \mathrm{X}_{1}, \mathrm{~L}\right)$
- $\left(\mathrm{q}_{4}, \mathrm{X}_{1}, \mathrm{R}\right)$
- $\left(\mathrm{q}_{1}, \mathrm{X}_{1}, \mathrm{R}\right)$
- Error Entry
(Option $1 [39689]) 1$
(Option $2 [39690]) 2$
(Option $3 [39691]) 3$
(Option $4 [39692]) 4$
Answer Given by Candidate: $1$
