3. Prove that the following propositions are true:

(e) For every integer n, 3n + 2 is even if and only if n + 5 is odd.

(f) For any integers x and y, max(x, y) + min(x, y) = x + y. Clarification: max is a function that returns the largest value, min is a function that returns the smallest value.

(g) If a real number r is not an integer, then there is an integer n in the interval (r 1, r) Clarification: the interval (r 1, r) consists of all real numbers x such that x > r 1 and x < r

(h) For any real number r, there exist unique numbers n and such that r = n + , n is an integer, and 0 < 1. Hint: The proposition from question 3g can be helpful.