MHB Math Logic: Equivalency, Validity, and Consequence

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Equivalence, validity, and consequence are key concepts in mathematical logic. Two formulas A and B are considered logically equivalent if the statement A if and only if B (A ↔ B) is valid. Validity refers to a formula being true in all interpretations, while consequence indicates that if A is true, then B must also be true. Understanding these relationships is crucial for grasping logical reasoning in mathematics. Clarifying definitions from the course can further aid in comprehending these concepts.
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.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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