Answered: Prove ⊢ (¬A → A) → A in Hilbert…

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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3. Prove ⊢ (¬A → A) → A in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). You may not use theorem 3.31, as this is precisely that theorem.Theorem 3.20 ⊢ ¬A → (A → B). Theorem 3.21 ⊢ A → (¬A → B). Theorem 3.22 ⊢ ¬¬A → A. Theorem3.23 ⊢A→¬¬A.Theorem3.25 ⊢(A→B)→(¬B→¬A).Theorem3.28 ⊢(¬A→false)→A.Rule 3.29 (Reductio ad absurdum) Theorem3.30 ⊢(A→¬A)→¬A.

Prove {¬A} ⊢ (¬B → A) → B in H. Note: In addition to the axioms and rule of inference of Hilbert deductive system, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook).

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