Probably pretty simple for ya'll but

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SUMMARY

The discussion revolves around a logic problem presented by a UMass student involving quantifiers and logical expressions. The specific expressions are ∀xFx V ∀xGx and the goal is to show that ∀x(Fx V Gx). The key to solving this problem lies in understanding the semantic definitions of quantifiers and identifying the conditions under which the conclusion would be false. The discussion emphasizes the importance of grasping these concepts to effectively approach similar logic problems.

PREREQUISITES
  • Understanding of first-order logic and quantifiers
  • Familiarity with logical expressions and their semantics
  • Knowledge of proof systems in formal logic
  • Basic skills in logical reasoning and problem-solving
NEXT STEPS
  • Study the semantic definitions of quantifiers in first-order logic
  • Learn about different proof systems, such as natural deduction and sequent calculus
  • Practice solving similar logic problems involving quantifiers
  • Explore counterexamples to understand when logical conclusions can fail
USEFUL FOR

Students of logic, educators teaching formal logic, and anyone interested in enhancing their understanding of quantifiers and logical proofs.

kshan5
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So I just got out of my intro to logic final at UMass and there was one question I just couldn't solve, and I'd like to know how. Anyways, here it is,

1. ∀xFx V ∀xGx
2. Show: ∀x(Fx V Gx)


I did 90% of the exam in a half hour, then spent the next hour on this alone and couldn't really get that close. Anyways, just really curious how you'd go about doing it.

Thanks.
 
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Show how? By using the quantifier's semantic definitions or were you asked to use a particular proof system? Anyway, in the former, here's a hint: what must happen for the conclusion to be false?
 

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