Using contrapositive method, prove the following. (i) For any integer n, if n 2 − 6n + 5 is even then n is odd. (ii) For any integers a and b, if a + b is even then a and b are even. (iii) For any integer n, if n 2 is odd then n is odd. (iv) For any integers a and b, if a 2 (b + 3) is even then a is even or b is odd. (v) For any positive integers n,r and s, if rs ≤ n then r ≤ √ n or s ≤ √ n. (vi) Let x and y are real numbers. If y 3 + 3yx2 ≤ x 3 + 3y 2x then y ≤ x. (vii) Let a be an integer. If a 2 is not divisible by 4 then a is odd.
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