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How can Euler circles be used to test whether a syllogism is valid?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Applied logic Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

Euler circles, or Euler diagrams, are a graphic method used to represent relations between classes—such as inclusion, exclusion, and intersection—to test the validity of a syllogism.12

In this method, the interior areas of circles represent concepts or properties. To test a syllogism, one draws circles to represent the premises. For example, to display the universal affirmative proposition "All A are B," one draws a circle labeled "A" entirely contained within a circle labeled "B". By manipulating these circles to visualize the relationships defined by the premises, one can determine if the conclusion follows necessarily. If the conclusion is represented by the resulting diagram, the syllogism is valid; if not, it is invalid.3

While Euler diagrams were popularized in the 18th century, they were not developed extensively by Euler himself and are often compared to Venn diagrams, which provide a more systematic approach using shading and symbols to represent categorical propositions and test deductive arguments.123