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Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y 149 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 149. Suppose, to the contrary, that both x and y are even. Then x = |k₁ + (3k₁ +5k₂) is ---Select--- 149 3x + 5y = K₂ = But 149 = 2. for some integer k₁ and y= +1 is also-Select--- for some integer K₂. Then This contradicts Axiom 1.2.

Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y 149 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 149. Suppose, to the contrary, that both x and y are even. Then x = |k₁ + (3k₁ +5k₂) is ---Select--- 149 3x + 5y = K₂ = But 149 = 2. for some integer k₁ and y= +1 is also-Select--- for some integer K₂. Then This contradicts Axiom 1.2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y = 149 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 149. Suppose, to the contrary, that both x and y are even. Then x = (3k₁ + 5k₂) is ---Select---- 149 3x + 5y = |k₂ = But 149 = 2. for some integer k₁ and y = for some integer k₂. Then + 1 is also ---Select--- . This contradicts Axiom 1.2.
Transcribed Image Text:Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y = 149 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 149. Suppose, to the contrary, that both x and y are even. Then x = (3k₁ + 5k₂) is ---Select---- 149 3x + 5y = |k₂ = But 149 = 2. for some integer k₁ and y = for some integer k₂. Then + 1 is also ---Select--- . This contradicts Axiom 1.2.
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