2. (12 points) The Kleene star is an operation which, on input a set of strings A, outputs a new set of strings (that we call A*) which is defined recursively by Basis step: A. Recursive step: If u is in A'and v is in A, then uv E A Note: when we write A we mean the empty string (see definition on page 349) and when we write uv we mean the string concatenation of u and v. The formal definition is Definition 2 on page 350. For each of the following sets, give an example of a nonempty bit string that is an element of the set, and give an example of a nonempty bit string that is not an element of the set (make sure to label which is which). If it is not possible to give these two examples, say so and explain why. (a) f01}" (b) (0,11,000) (c) fo*U1) (d) 1001)* n 001001* (e) 0