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Consider a proof system P in the style of box-proof which only have one logical connective A. The system only has one rule given by:

Consider a proof system P in the style of box-proof which only have one logical connective A. The system only has one rule given by:

Database System Concepts
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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Consider a proof system P in the style of box-proof which only have one logical connective A. The system only has one rule given by: [X] Y YAX Here, X and Y can represent any formula. Tick each that applies. In the proof system P it is possible to derive the formula ((AAC)AB)AA In the proof system P it is possible to derive AA(AA A) In the proof system P it is possible to derive the formula AAA In the proof system P it is possible to derive (AAA)^ A In the proof system P it is not possible to derive (AA B)A(BAA)
Transcribed Image Text:Consider a proof system P in the style of box-proof which only have one logical connective A. The system only has one rule given by: [X] Y YAX Here, X and Y can represent any formula. Tick each that applies. In the proof system P it is possible to derive the formula ((AAC)AB)AA In the proof system P it is possible to derive AA(AA A) In the proof system P it is possible to derive the formula AAA In the proof system P it is possible to derive (AAA)^ A In the proof system P it is not possible to derive (AA B)A(BAA)
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