Discrete Math Question

3. Suppose S is the set of bit strings recursively defined by: 001 E S beS - 11beS be S - 10be S bES- 1beS. Let ca the number of bit strings in S of length n for n 2 2. This problem superficially looks very similar to problem 2, only the 3rd recursion rule is slightly different. . (2 points) Would be c, the same as a, in problem 2 for all integer n. n > 27 . (2 points) Can we use the same idea to construct a recurrence relation for ca that we used in problem 2 for an? Explain your answer for each question. (Hint: find as and cs.)