Problem 3. Let S be the set of all binary strings that have an even number of ls. (a) For k > 0, let Sk be the set of all binary strings that have exactly k occurrences of 1. Find a rational expression for Sx(x), where the weight of a string is its length. (b) Give a formula for the number of strings in Sk of length n when n > k and k > 1. (c) Let S be the set of all binary strings with an even number of ls. Find a rational expression for Os(x). Problem 3. Let S be the set of all binary strings that have an even number of ls. (a) For k > 0, let Sk be the set of all binary strings that have exactly k occurrences of 1. Find a rational expression for Sx(x), where the weight of a string is its length. (b) Give a formula for the number of strings in Sk of length n when n > k and k > 1. (c) Let S be the set of all binary strings with an even number of ls. Find a rational expression for Os(x)