(2) Determine whether each of the following statements are true or false and prove your conjectures:...

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(2) Determine whether each of the following statements are true or false and prove your conjectures: (a) For every integer n, 5n + 4n + 3n+ 2 is an even integer. (b) If a, b, c, d are integers with a - bd is divisible by 6. - - b divisible by 2 and c - d divisible by 3, then (c) If x and y are irrational numbers, then x + y or x - y is an irrational number. (d) For every real number x, there is a real number y such that x y is rational. (2) Determine whether each of the following statements are true or false and prove your conjectures: (a) For every integer n, 5n + 4n + 3n+ 2 is an even integer. (b) If a, b, c, d are integers with a - bd is divisible by 6. - - b divisible by 2 and c - d divisible by 3, then (c) If x and y are irrational numbers, then x + y or x - y is an irrational number. (d) For every real number x, there is a real number y such that x y is rational.