Closure in Reverse $[7$ points$]$

Suppose that L is an arbitrary regular language. Prove that L

R$,$ the reverse of L$,$ is also regular.

If a string w is in L$,$ the reverse of that string, w

R$,$ is in L

R$.$ The reverse operation is defined recursively as:

$\backslash$epsi

R $=\backslash$epsi

$$ For a string w and symbol a in $\backslash$Sigma $,($wa$)$

R $=$ a$($w

R$)$

i$.$e$.(110)$R $=011.$