4. Closure in Reverse [7 points] Suppose that L is an arbitrary regular language. Prove that LR, the reverse of L, is also regular. If a string w is in L,

the reverse of that string, w, is in LR. The reverse operation is defined recursively as: • ER = E For a string w and symbol a € E, (wa) = a(w) i.e. (110) R = 011.