We introduce the rotation operation on languages rot$($L$)=\{$xy$|$yx in L$\}.($a$)(10$ points$)$ Show that rot$($L$)=$rot$($rot$($L$))).$ Start to show that rot$($L$)$rot$($rot$($L$)).$ Then,show rot$($L$)$rot$($rot$($L$)).($b$)(15$ points$)$ Show that a regular language L is closed under the operation rot$().$ Let ML be aDFA that recognizes L$.$ Show how to build a NFANLthat recognizesrot$($L$)$