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A classroom has two rows of eight seats each. There are 14 students, 5 of whom always sit in the front row and 4 of whom always sit in the back row. In how many ways can the students be seated? Show the validity of the following argument: Prove that: Let c_i elementof Z, for 1 lessthanorequalto i lessthanorequalto n. If a divides each c_i, then a|(c_1 x_1 + c_2 x_2 + .. + c_n x_n) where x_i elementof Z for all 1 lessthanorequalto i lesthanorequalto n. Define the greatest common divisor and the least common multiple of two integers. What is the relation between the greatest common divisor and the least common multiple? What is the logical statement? What is the symmetric difference of two sets? What is the principle of mathematical induction