$(20$ pts$)$ Let $x=\{ab,$bbba$\}$ be a language over the alphabet $=\{a,b\}$ and let $$ be a morphic

involution with $(a)=b$ and $(b)=a.$ For every true statement below present a proof.

Otherwise, present a counterexample. Use the respective definitions. Determine whether:

$($a$)x$ is a $-$infix code

$($b$)x$ is a $-$comma$-$free

$($c$)x$ is a $-$subword$-2$ code

$($d$)x$ is a $-3$ code. Is $x$ is a $-2$ code? Is $x$ is a $-4$ code?