Math Logic: Equivalency, Validity, and Consequence

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  • Thread starter Thread starter hossam killua
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SUMMARY

The discussion centers on the relationship between equivalence, validity, and consequence in mathematical logic, specifically in the context of an introductory course. It is established that two formulas, denoted as $A$ and $B$, are logically equivalent if and only if the formula $A \leftrightarrow B$ is valid. This highlights the foundational concepts of logical equivalence and validity as critical components in understanding mathematical reasoning.

PREREQUISITES
  • Understanding of basic mathematical logic concepts
  • Familiarity with logical formulas and symbols
  • Knowledge of validity in logical arguments
  • Introduction to logical equivalence
NEXT STEPS
  • Study the definitions and examples of logical equivalence in mathematical logic
  • Explore the concept of validity and its implications in logical reasoning
  • Learn about logical consequence and its relationship to equivalence
  • Review formal proofs involving equivalence and validity
USEFUL FOR

Students in introductory mathematical logic courses, educators teaching logic concepts, and anyone seeking to deepen their understanding of logical relationships in mathematics.

hossam killua
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i take introduction math logic course in college and professor

ask for relation between equivalent and valdity and consequence

can u help??
 
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It's difficult to say what you mean without knowing more context. Could you provide the definitions of equivalence, validity and consequence that are used in your course?

One possible answer to your question is that two formulas $A$ and $B$ are logically equivalent iff the formula $A\leftrightarrow B$ is valid.
 

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