How to find a logical statement equivalent to the one I have?

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SUMMARY

The logical statement (A ∧ B) ⇔ (A ∧ C) can be transformed into equivalent forms without the use of truth tables. A valid equivalent statement is (A ∧ (B ⇔ C)). Users can reference the Wikipedia page on propositional logic for a comprehensive list of valid argument forms and derived theorems. This approach allows for substitution of variables to explore further equivalences in logical statements.

PREREQUISITES
  • Understanding of propositional logic
  • Familiarity with logical equivalences
  • Knowledge of logical connectives (∧, ∨, ⇒, ⇔)
  • Ability to interpret logical statements and their transformations
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  • Research "Logical equivalences in propositional logic"
  • Study "Theorems of propositional logic" for deeper insights
  • Explore "Substitution methods in logical statements"
  • Review "Valid argument forms in propositional logic" on Wikipedia
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Students of mathematics, logic enthusiasts, and anyone looking to deepen their understanding of logical statements and their equivalences.

omoplata
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I have the following logical statement
(A \wedge B) \Longleftrightarrow (A \wedge C)
I want to find other logical statements that are equivalent to this. But I don't want to draw truth tables.

Is there a list of 'theorems' that I can look up somewhere? For example, if I have an equivalent statement for D \Longleftrightarrow (A \wedge C), then I can maybe substitute D = (A \wedge B) and maybe come up with something.

Sorry if my terminology is wrong. Logic is not exactly my subject.
 
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That helps. Thanks.
 
I am pretty sure that this is equivalent:
( A \wedge ( B \leftrightarrow C ) )
 

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