$1.(10$ pts$)$ Construct a Turing machine that accepts the language $\backslash ($ L$=\backslash \{$w $\backslash$mid w $\backslash )$ is a palindrome over $\backslash (\backslash \{0,1\backslash \}\backslash \}\backslash )$

$2.(10$ pts$)$ Design a Turing Machine $($TM$)$ that decides whether a given string belongs to the language $\backslash ($ L $\backslash ).$

$-$ Describe the states, transitions, and how the Turing Machine will operate step by step for a sample input.

$-$ Include a diagram of the Turing Machine or a clear state transition table.