Let REVERSE(L) represent the reverse of L, defined as: (w: wis in L and wR is the reverse of w). For example, REVERSE(("ab", "bba") is ("ba", "abb" It is known that for any languages Li and L2, the following is true: REVERSEL1) (REVERSEL)* REVERSE(LI U L2)-REVERSE(LI) U REVERSE( REVERSE(Li o L2) = REVERSE(2) o REVERSE(LI) Use these facts to prove with a recusive proof,that if L is regular, then REVERSE(L) is also regular. Hint: start with the fact that if L is regular, there must be some RE that specifies it