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.
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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 7TFE: True or false
Label each of the following statement as either true or false.
Let and be integers,...
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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.
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