Let SW AP $($L$)=\{$ywx $|$ xwy in L$,$ x$,$ y in $\backslash$Sigma $,$ w in $\backslash$Sigma $\},$ i$.$e$.$ the set of strings from L$,$

but with their first and last letters swapped. This means that if L $=\{$cat$,$ dog$\},$ then

SW AP $($L$)=\{$tac$,$ god$\}.$

Prove that if L is a regular language, then SW AP $($L$)$ must also be regularLet SWAP$(L)=\{ywx|xwyinL,x,$yin$,$win${}^{**}\},$ i$.$e$.$ the set of strings from $L,$

but with their first and last letters swapped. This means that if $L=\{cat,$dog$\},$ then

$,$ god