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...


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

Extracted 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)

Jun 09, 2022
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