Only number 5. 4. Explain what is wrong in the following "proof."CLAIM. Let x be a real number. If x is irrational, then 2x is irrational."PROOF." Take r =is irrational for any irrational number c.V2. Then x is irrational, and so is 2x = 2/2. Therefore 2x%3D%3D(Note. Find the mistakes in logical reasoning. "Lacks detail is not a mistake.)5. Give a complete proof by contradiction of the claim in item 4. (Recall. A numberis rational iff it can be written as the quotient of two integers.)

Answered: Image /qna-images/answer/8bccc012-0bd4-410a-bf68-c24c7b64e1a9.jpg

4. Explain what is wrong in the following "proof." CLAIM. Let x be a real number. If a is irrational, then 2x is irrational. "PROOF." Take r = V2. Then r is irrational, and so is 2x = 2/2. Therefore 2x is irrational for any irrational number c. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.) 5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number is rational iff it can be written as the quotient of two integers.)

4. Explain what is wrong in the following "proof." CLAIM. Let x be a real number. If a is irrational, then 2x is irrational. "PROOF." Take r = V2. Then r is irrational, and so is 2x = 2/2. Therefore 2x is irrational for any irrational number c. (Note. Find the mistakes in logical reasoning. "Lacks detail" is not a mistake.) 5. Give a complete proof by contradiction of the claim in item 4. (Recall. A number is rational iff it can be written as the quotient of two integers.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...

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