For words, w$,$ u$,$ v in $,$ if we can write w $=$ uv$,$ then we can define a cyclic shift of the w as vu$.$ For example, the word w $=$ abca has four cyclic shifts: bcaa, caab, aabc, and abca. Define c$($w$,$ k$)$ to be the $($left$)$ cyclic shift by k symbols. So$,$ c$($abca$,0)=$ abca, c$($abca$,1)=$ bcaa, c$($abca$,2)=$ caab, and c$($abca$,3)=$ aabc. For any language L$,$ we define CS$($L$)=\{$x : x in L and c$($x$,$ k$)$ in L$,0$ k $<|$x$|\}.$ For example, if L $=\{$a$,$ b$,$ ba$,$ ab$,$ bbb$,$ aba, aab$\},$ then CS$($L$)=\{$a$,$ b$,$ ab$,$ ba$,$ bbb$\},$ since a $=$ c$($a$,0)$ and b $=$ c$($b$,0),$ ab $=$ c$($ba$,1)$ and ba $=$ c$($ab$,1),$ and bbb $=$ c$($bbb$,0)=$ c$($bbb$,1)=$ c$($bbb$,2).$ Note that c$($aba$,1)=$ c$($aab$,2)=$ baa $$ in L$,$ and thus aba $$ in CS$($L$)$ and baa $$ in CS$($L$).($a$)$ If L is recursive, is CS$($L$)$ also recursive? Justify your answer. $($b$)$ If L is recursively enumerable, is CS$($L$)$ also recursively enumerable? Justify your answer.