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April 19, 2024

King saud discrete math

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.

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