quesition4 3. Consider the structure R =(IR, +, ×, <). We say that a set C CR is definable in R ifthere is a formula p(x) such that c E C if and only if p[c] is true in R. Show that the setC = {0,1} is definable in R.(Hint: Consider the polynomial whose solution is exactly 0 or 1.)4. Consider again the structure R(IR, +, ×, <) and let P(x, y) be the predicate x < y.Express the predicate using a formula p(x, y) involving only + and × and not involving <.That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in Rwith p(x, y) not involving the symbol <.

The solution for the above given question is given below:

4. Consider again the structure R = (IR, +, x, <) and let P(x, y) be the predicate a < y. Express the predicate using a formula p(x, y) involving only + and x and not involving <. That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R with p(x, y) not involving the symbol <.

4. Consider again the structure R = (IR, +, x, <) and let P(x, y) be the predicate a < y. Express the predicate using a formula p(x, y) involving only + and x and not involving <. That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R with p(x, y) not involving the symbol <.

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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