3. (standard, 20pt) Let & be an alphabet. Given two words wi and W2, a match between w and W2 is a word w satisfying w1 = W'w and W2 = ww, for some w1 and wa. Given two languages L and L2, we use LiVL2 to denote the set of matches between Wi and W2 for all wi E L1, W2 E L2. Prove that if L and L2 are regular languages, then so is Li VL2