$($a$)$

$($b$)$ State, with brief justification, what language the Turing machine decides, or that it does

not decide any language.

$($c$)$ State, with brief justification, how a small number of the Turing machine's state transitions

can be modified so that it accepts just the even$-$length strings that the original Turing

machine accepts, and rejects everything else. $($You may modify only the transitions; do

not add or remove any states.$)$