answer this including step by step solution

Turing machines

Consider the Turing machine M$6$ below.The input alphabet to this machine is $\{1,2,3,4\}.$

$($a$)$ What is $L(M)?$ Show some examples of strings accepted and rejected to justify your answer.

You must show at least one accepted string of length at least $6,$ and at least one rejected string

of length at least $6.$

$($b$)$ Consider the Turing machine $M_7$ obtained from $M_6$ by adding the transitions $(q_4,x)=(x,L,q_5)$

for xin$\{2,3,4\}.$ Is $M_7$ equivalent to $M_6?$ Explain your answer.

$($c$)$ Consider now the Turing machine $M_8$ obtained from $M_6$ by adding the transitions $(q_0,x)=$

$(x,R,q_1)$ for xin$\{3,4\}.$ Is $M_8$ equivalent to $M_6?$ Explain your answer.