Order the following sentences so that they form a direct proof of the statement: If x and y are rational numbers, then 3x + 2y is also a rational number. Choose from this list of sentences Since b, d are integers, bd is an integer. By the definition of rational numbers, x = alb where a and b are integers and b 0, and y = c/d where c and d are integers and d 0. Since 3x + 2y can be expressed as a ratio of two integers where the denominator is not zero, 3x + 2y is a rational number. Since a, b, c, d are integers, 3ad + 2bc is an integer. Let x and y be rational numbers. Since b 0 and d # 0, bd # 0. It follows that 3x + 2y = 3a/b + 2cld = (3ad +2bc)/(bd) Direct proof of the statement (in order):

Order the following sentences so that they form a direct proof of the statement: If x and y are rational numbers, then 3x + 2y is also a rational number. Choose from this list of sentences Since b, d are integers, bd is an integer. By the definition of rational numbers, x = alb where a and b are integers and b 0, and y = c/d where c and d are integers and d 0. Since 3x + 2y can be expressed as a ratio of two integers where the denominator is not zero, 3x + 2y is a rational number. Since a, b, c, d are integers, 3ad + 2bc is an integer. Let x and y be rational numbers. Since b 0 and d # 0, bd # 0. It follows that 3x + 2y = 3a/b + 2cld = (3ad +2bc)/(bd) Direct proof of the statement (in order):

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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