Problem #4 (20 points) a) Give a direct proof to show that if x is an even integer, then x+x is an even integer. b) Show that if n is an integer and n +5 is odd, then n is even using a proof by contraposition. c) Prove that if n is an integer and 3n+2 is even, then n is even using a proof by contradiction. d) Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd. e) Prove using contrapositive method that for all real numbers x and y, if x+y2100, then (x250 or y250)