How to Prove Predicate Logic Validity with Induction?

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SUMMARY

The discussion focuses on proving the validity of a predicate logic argument using the induction method. The specific argument presented is (∃x)[P(x)!Q(x)]^(∀y)[Q(y)!R(y)]^(∀x)P(x)!(∃x)R(x). Participants emphasize the importance of showing progress in problem-solving to facilitate effective assistance. Additionally, the symbol "!" is questioned, indicating a need for clarification on its meaning within the context of the argument.

PREREQUISITES
  • Understanding of predicate logic and its symbols, particularly existential and universal quantifiers.
  • Familiarity with mathematical induction as a proof technique.
  • Knowledge of logical connectives, specifically implications and conjunctions.
  • Basic experience with formal logic notation and expressions.
NEXT STEPS
  • Study the principles of mathematical induction in formal logic proofs.
  • Learn about the interpretation of logical symbols, particularly the meaning of "!" in this context.
  • Explore examples of proving validity in predicate logic using induction.
  • Review the structure of logical arguments and how to manipulate them for proof purposes.
USEFUL FOR

Students of mathematics, logic enthusiasts, and anyone interested in mastering proof techniques in predicate logic.

Voehet
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How would I go about proving that the argument below is valid using the induction method?
(∃x)[P(x)!Q(x)]^(∀y)[Q(y)!R(y)]^(∀x)P(x)!(∃x)R(x)

Thank you very much in advance!
 
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Hello and welcome to MHB, Voehet! :D

We ask that our users show their progress when posting questions, and that way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
Voehet said:
How would I go about proving that the argument below is valid using the induction method?
(∃x)[P(x)!Q(x)]^(∀y)[Q(y)!R(y)]^(∀x)P(x)!(∃x)R(x)
What does ! stand for?
 

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