1. True or False. [5 points each (a) The intersection of any two regular languages is regular. (b)If L is any regular language, define PREF(L) to be the set of all prefixes of strings in L. (A prefix of a string u is a substring consisting of the first k symbols of w for some k.) Then PREF(L) is regular. (c) (d) Every subset of a regular language is regular. If h is a homomorphism -+ r, and if L is a language over such that h(L) is regular, then L must be regular. (e)Let M be a finite state machine with both input and output, where the input alphabet is and the output alphabet isLet L be a regular language over , and let M(L) be the language over T consisting of all possible output strings providing the input string is in L. Then M(L) must be regular