Let L be a language. Define Pref(L) = {w * x = wy for some Ly }l In words it is the set of all prefixes of strings in L. For example, if L = L(abaa U b)") then Pref(L) = {a, ab} UL. (a) Suppose L = {0"1"in >0}. What is Pref(L.)? (6) Suppose II = {wwewe {a,b}'). What is Pref(L')? (c) Show that if L is regular, then so is Pref(L). Hint I suggest you start with a DFSM M, such that L(M) = L and show how to modify M to accept Pref(L), A major part of your grade on this problem will be based on an argument that your new machine accepts exactly Pref(L). A proof by induction is not required. A good intuitive explanation of why each direction of the inclusion holds will suffice