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 'Value of intuitionistic logic'

I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
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