Given a DFA, M, with alphabet, sigma, and a string s = s_1 s_2 s_3 ... s_100 that is in L(M). Prove that if the number of states in M is 10, then there must be a substring between s_45 and s_65 that can be repeated an arbitrary number of times and the so modified string will still be in L(M). Given a DFA, M, with alphabet, sigma, and a string s = s_1 s_2 s_3 ... s_100 that is in L(M). Prove that if the number of states in M is 10, then there must be a substring between s_45 and s_65 that can be repeated an arbitrary number of times and the so modified string will still be in L(M)