Analyze the following "proof" and determine if there is anything incorrect and why. Claim. Let x be a real number. If x is irrational, then 2x is irrational. “Proof." Suppose that 2x is rational. Then there exist integers p and q, with q + 0, such that 2x = 2. Thus, x = where p and 2q are integers and 2g + 0. So x is rational. We conclude that if x is irrational, then 2x is irrational.

Analyze the following "proof" and determine if there is anything incorrect and why. Claim. Let x be a real number. If x is irrational, then 2x is irrational. “Proof." Suppose that 2x is rational. Then there exist integers p and q, with q + 0, such that 2x = 2. Thus, x = where p and 2q are integers and 2g + 0. So x is rational. We conclude that if x is irrational, then 2x is irrational.

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Description: Analyze the following "proof" and determine if there is anything incorrect and why.Claim. Let x be a real number. If x is irrational, then 2x is irrational."Proof." Suppose that 2x is rational. Then there exist integers p and q, with q # 0, such tha

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Analyze the following "proof" and determine if there is anything incorrect and why.
Claim. Let x be a real number. If x is irrational, then 2x is irrational.
"Proof." Suppose that 2x is rational. Then there exist integers p and q, with q # 0, such that 2x = 2. Thus, x =
where p and 2q are integers and 2g + 0. So x is rational. We conclude that if x is irrational, then 2x is irrational.
2q
Q.E.D.

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