Q1- Use a proof by contraposition to show that if x y≥2 where x and y are real numbers, then x≥1 or y≥1. Q2- Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers. Q3- Let n be a positive integer. Prove that n is odd if and only if 5n 6 is odd. Q4- Prove that there are no positive perfect cubes less than 1000 that are the sum of the cubes of two positive integers. Q5- Prove that there are no solutions in integers x and y to the equation 2𝑥 2 5𝑦 2 =14.