3. [5 + 1520 points) A VFA is defined as a 5-tuple M = (0,4,8,90, F) exactly as an NFA. However, the acceptance is defined differently. An NFA accepts a string w if there is an accept state that can be reached from go while reading the input w. A VFA accepts a string w if every state that can be reached from go while reading the input w is an accept state. (a) Prove that every regular language is recognized by a VFA. (b) Prove that every VFA recognizes a regular language