Problem #4 (40 points) a) Give a direct proof to show that if x is an even integer, then xx is an even integer b) Show that if a is an integer and w+5 is odd, then is even using a proof by contraposition. c) Prove that if n is an integer and 3m+2 is even, then n is even using a proof by contradiction d) Prove that if n is apositive integer,then n is odd if and only if Sn+6 is odd e) Prove using contrapositive method that for all real numbers x and y, if x y2100, then (x250 or yeso)