Denote the sentence \x(x = x) by T (for Truth) and let Ƒ := ¬T (for Falsity), so in everyo-structure, T is true and Ƒ is false. Prove that for a o-theory T, the following areequivalent:(1) T is satisfiable.(2) TE F.(3) There is some o-sentence o such that T * 9.

The question is based on the equivalence of three statements within the context of formal logic and…

Denote the sentence Vx(x = x) by T (for Truth) and let Ƒ := ¬T (for Falsity), so in every o-structure, T is true and F is false. Prove that for a o-theory T, the following are equivalent: (1) Tis satisfiable. (2) TE F. (3) There is some o-sentence p such that TQ.

Denote the sentence Vx(x = x) by T (for Truth) and let Ƒ := ¬T (for Falsity), so in every o-structure, T is true and F is false. Prove that for a o-theory T, the following are equivalent: (1) Tis satisfiable. (2) TE F. (3) There is some o-sentence p such that TQ.

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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Question

Denote the sentence \x(x = x) by T (for Truth) and let Ƒ := ¬T (for Falsity), so in every
o-structure, T is true and Ƒ is false. Prove that for a o-theory T, the following are
equivalent:
(1) T is satisfiable.
(2) TE F.
(3) There is some o-sentence o such that T * 9.

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