The Star Method for Testing Syllogisms

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I'm working though Introduction to Logic by Harry Gensler in which he presents his own invention for testing syllogisms-the star method. I was wondering how common this method is in comparison to Venn diagram methods. It's much quicker than Venn diagrams to use, but the beginning student is at a loss as to why it works. Gensler suggests its validity is a topic for more experienced logicians.
 
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