Prove that if L is a regular language over an alphabet , then, in first-order statement, Vy * positive integers m, n [(m > n) ^ \z * (ym z L if and only if y" z L)]. Use the above result to study the regularity of the following languages: (a) L = {0 | i > 0}. (b) L = {uurv | u, v = (a + b)+}.