1. [25 points] Let M be the DFA having the state diagram 40 9i 42 Answer the following questions, giving a brief explanation of your answer. (One short sentence, or perhaps even a sentence fragment, will suffice.) (a) Is (M,001011001) E ADFA? (b) Is(M. 0010110011) ADFA? (c) Is(M) EDFA? (d) Is (M,M) E EQDFA? (e) Let R-0"(10). 110"(10), 1( 10.1)*. Is(R001011001)EAREX? Hint: Why did I choose this regular expression to be part of this problem? whether a FA accepts a string (ADFA), whether an NFA accepts a string (ANFA), whether a regular expression accepts a string (AREX). whether the language of a FA is empty (EDFA), whether two FA are equivalent (EQDFA)