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

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Discussion Overview

The discussion revolves around finding logical statements that are equivalent to a given logical expression, specifically (A ∧ B) ↔ (A ∧ C). Participants explore methods to identify such equivalents without resorting to truth tables.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks equivalent logical statements for (A ∧ B) ↔ (A ∧ C) and expresses a preference for not using truth tables.
  • Another participant suggests a resource, specifically a Wikipedia table of valid argument forms in propositional logic, as a potential aid in finding equivalents.
  • A later reply proposes that (A ∧ (B ↔ C)) is an equivalent statement, although this claim is not universally accepted or confirmed by others in the thread.

Areas of Agreement / Disagreement

There is no consensus on the equivalence of the proposed statements, and the discussion includes differing approaches to finding logical equivalents.

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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