Problem 1. [25 points) The reverse of a string a over an alphabet , denoted at, is defined inductively by ET = e and, for a EE and we 2*, by (aw)T = wa. The reverse of a language L over an alphabet ? is the language LT = {WT: WE L}. Is it always true that the reverse of a regular language is regular? What of context-free languages: is IT always context-free whenever Lis context-free? Prove that your answers are is correct