Question: All please , a) Give a direct proof to show that if x is an even integer, then x+x is an even integer. b) Show

All please ,

a) Give a direct proof to show that if x is an even integer, then x+x is an even integer. b) Show that ifn is an integer and + 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 (250 or y250)

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