Question 5: In this exercise, we consider strings of characters, where esch character is an element of (a, b, c. For any integer n1, let En be the number of such strings of length n that have an even number of c's, and let On be the number of such strings of length n that have an odd number of c's. (Recall that 0 is even) Determine E1, 0, E2, and O2 Explain in plain English and at most two sentences why . Prove that for every integer n2 En = 2 . En-1 +0,-! . Prove that for every integer n, 1 +3n En =