Proofs, ie. Contrapositive, contradiction, and cases.

Need help solving these problems.

2. Prove each of the following statements using proof by contrapositive. (a) For every positive integer n, if n2-2n7 is even, then n is odd. (b) Given that r and y are real numbers, if r +y > 20, then > 10 or y >10. Prove each of the following statements using proof by contradiction. (a) There is no smallest integer. (b) Given that n is an integer, show that n2 +1 is not divisible by 8. 3 (Hint: you can use the theorem: If n2 is odd, n is odd.) 1. Prove each of the following statements using the method of proof by cases. (a) The parity of a number tells whether the number is odd or even. If r and y have the same parity, they are either both even or both odd. If integers r and y have the same parity, then r + y is even (b) For any real number x, Ir12 max(x,-r)