Answered: Define the set U = {x ∈ Z | ∃y ∈ Z, xy…

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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Define the set U = {x ∈ Z | ∃y ∈ Z, xy = 1} = {+1, -1}. We say a number p ∈ Z \ {0} is prime if and only if p ∉ U and ∀a ∈ Z, ∀b ∈ Z, p|ab ⇒ (p|a ∨ p|b). (intuitively this says you can’t build a prime p by combining things which do not already contain p)

We say a number i ∈ Z is irreducible if and only if ∀a ∈ Z, ∀b ∈ Z, i = ab ⇒ (a ∈ U ∨ b ∈ U) (intuitively this says p is irreducible if the only things which divide it are 1 and p (and -1, and -p).)

Prove that if x = ab ≠ 0 and x|a then b ∈ U.

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