Solution Found!
Find the mistakes in the “proofs” that the sum
Chapter 4, Problem 37E(choose chapter or problem)
In 35–39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
“Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b \(\neq\) 0, and s = a/b for some integers a and b with b \(\neq\) 0. Then
\(r+s=\frac{a}{b}+\frac{a}{b}=\frac{2 a}{b}\)
Let p = 2a. Then p is an integer since it is a product of integers. Hence r + s = p/b, where p and b are integers and b \(\neq\) 0. Thus r + s is a rational number by definition of rational. This is what was to be shown.”
Text Transcription:
neq
r + s = a/b + a/b = 2a/b
Questions & Answers
QUESTION:
In 35–39 find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.
“Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b \(\neq\) 0, and s = a/b for some integers a and b with b \(\neq\) 0. Then
\(r+s=\frac{a}{b}+\frac{a}{b}=\frac{2 a}{b}\)
Let p = 2a. Then p is an integer since it is a product of integers. Hence r + s = p/b, where p and b are integers and b \(\neq\) 0. Thus r + s is a rational number by definition of rational. This is what was to be shown.”
Text Transcription:
neq
r + s = a/b + a/b = 2a/b
ANSWER:Solution:Step 1 of 3 :In this problem we have to find the mistakes in “proofs’’ that the sum of any two rational numbers is a rational number.