Write a proof by contradiction of the following. Let x and y be integers. If x and y satisfy the equation 3x + 5y = 153 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 153. Suppose, to the contrary, that both x and y are even. Then x = (3k₁+5k₂) is -Select-- 153 = 3x + 5y = K₂ = . But 153 = 2 for some integer k₂ 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 = 153 then at least one of x and y is odd. Let x and y be integers that satisfy the equation 3x + 5y = 153. Suppose, to the contrary, that both x and y are even. Then x = (3k₁+5k₂) is -Select-- 153 = 3x + 5y = K₂ = . But 153 = 2 for some integer k₂ and y = +1 is also --Select--- for some integer k₂. Then This contradicts Axiom 1.2.
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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the options are even or odd.
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 = 153
then at least one of x and y is odd.
Let x and y be integers that satisfy the equation 3x + 5y = 153. Suppose, to the contrary, that both x and y are even. Then x =
(3k₁ + 5k₂) is ---Select----
153 = 3x + 5y =
. But 153 2.
for some integer k₁ and y =
+ 1 is also ---Select---
for some integer k₂. Then
This contradicts Axiom 1.2.
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