Prove the following theorems using direct proof, indirect proof(contradiction, contrapositive), counterexample, and/or proof by cases. 1. For every pair of positive real numbers x and y, if xy > 400,...

Prove the following theorems using direct proof, indirect proof(contradiction, contrapositive), counterexample, and/or proof by cases. 1. For every pair of positive real numbers x and y, if xy > 400, then x > 20 or y > 20. 2. For integers x and y. If xy is odd, then x is odd and y is odd.