Determine the validity of the ff. proof: Theorem: "the sum of any two rational numbers is a rational number" Proof: "Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b + 0, and s = a/b for some integers a and b with b + 0. Then 2a a r+s== b b a -- b Let p = 2a. Then p is an integer since it is a prod- uct of integers. Hence r+s = p/b, where p and b are integers and b + 0. Thus r + s is a rational number by definition of rational. This is what was to be shown."
Determine the validity of the ff. proof: Theorem: "the sum of any two rational numbers is a rational number" Proof: "Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b + 0, and s = a/b for some integers a and b with b + 0. Then 2a a r+s== b b a -- b Let p = 2a. Then p is an integer since it is a prod- uct of integers. Hence r+s = p/b, where p and b are integers and b + 0. Thus r + s is a rational number by definition of rational. This is what was to be shown."
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:Determine the validity of the ff. proof:
Theorem: "the sum of any two rational numbers is a rational number"
Proof:
"Proof: Suppose r and s are rational numbers. By
definition of rational, r = a/b for some integers
a and b with b + 0, and s = a/b for some integers
a and b with b + 0. Then
2a
a
r+s ==+
b b
a
- =
b
Let p = 2a. Then p is an integer since it is a prod-
uct of integers. Hence r+s = p/b, where p and b
are integers and b + 0. Thus r+ s is a rational
number by definition of rational. This is what was
to be shown."
Maybe
O Yes, it is valid
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Not valid
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