Syllogism
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Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.
What a syllogism is and how to test it
Transitivity of All
A \subset B \wedge B \subset C \Rightarrow A \subset C
'All A are B + All B are C → All A are C' is the only freely chained rule.
Conversion of All
\text{All } A \subset B \Rightarrow \text{Some } B \subset A
Valid (classes are assumed non-empty): 'Some B are A' follows.
Conversion of No / Some
\text{No } A \cap B \Leftrightarrow \text{No } B \cap A;\quad \text{Some } A \cap B \Leftrightarrow \text{Some } B \cap A
Both convert symmetrically.