Use either the soundness or the completeness (Post's theorem) of the propositional logic to prove ¬A V (B ^ C) Etaut (A → B) ^ (A → C). Which one did you use, soundness or completeness?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Use either the soundness or the completeness (Post's theorem) of the propositional logic to prove
¬A V (BA C) Ftaut (A → B) ^ (A → C). Which one did you use, soundness or completeness?
Transcribed Image Text:Use either the soundness or the completeness (Post's theorem) of the propositional logic to prove ¬A V (BA C) Ftaut (A → B) ^ (A → C). Which one did you use, soundness or completeness?
Expert Solution
Step 1

Soundness Theorem:

If P|-Q then P|=tautQ.

In words, soundness theorem says that if P implies Q then P tautologically implies Q.

Here,

  • P=~ABC
  • Q=ABAC

 

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