!! Exercise 4.2.10: Suppose that L is any language, not necessarily regular, whose alphabet is 10^; i.e., the strings of L consist of 0's only. Prove that L* is regular. Hint: At first, this theorem sounds preposterous. However, an example will help you see why it is true. Consider the language L-10'i is prime which we know is not regular by Example 4.3. Strings 00 and 000 are in L, since 2 and 3 are both primes. Thus, if j 2, we can show 0J Is in L*. If j is even, use j/2 copies of 00, and if j is odd, use one copy of 000 and (j - 3)/2 copies of 00. Thus, L*-+ 000