Prove the following: a. A positive integer n is divisible by 5 if and only if its last digit is O or 5 b. If x and y are rational numbers and y 0, then x/y is also rational. c. Let n be any integer. Prove by cases thatn is evenly divisible by 3 d. Let n E Z20. If 2n4 n5 is odd, then n is even. e. Suppose 12x+3y 254, for real numbers x and y. Then either x or y (or both) is not an integer. Prove the following: a. A positive integer n is divisible by 5 if and only if its last digit is O or 5 b. If x and y are rational numbers and y 0, then x/y is also rational. c. Let n be any integer. Prove by cases thatn is evenly divisible by 3 d. Let n E Z20. If 2n4 n5 is odd, then n is even. e. Suppose 12x+3y 254, for real numbers x and y. Then either x or y (or both) is not an integer