a. Using formal definitions distinguish between a path and a cycle. [4] b. State the Pigeonhole Principle. [3] c. How many ways can five of the letters of the word ALGORITHM be selected and written in a row if the first two letters must be TH? [4] d. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose six integers are chosen from A. Must there be two integers whose sum is 11. [4] e. Prove by mathematical induction for all integers n1. [8] Questio