Problem 5: Strong Induction [20 points] (a) Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. Prove that P(n) is true for all integer n such that n 2 20. (b) Let an be a sequence recursively defined as follows a,-3, a2-9, --3 and an+3--2@m+2 + a1+2an, n 1,2,3,.... Let P(n) be the statement: an 5(-2)". Prove that P(n) is true for all positive integer n