Venn Test: Valid Case
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The Venn test for a syllogism means diagramming both premises on three overlapping circles, then reading the diagram to see whether the conclusion is already drawn there without any further mark being added.
Take AAA-1. All M are P. All S are M. So all S are P. Three circles: S, P, and M, each overlapping the others. Diagram the major premise first. All M are P says nothing lives in the part of M that falls outside P, so shade that whole region. Now the minor premise. All S are M says nothing lives in the part of S outside M, so shade that too. Put the pencil down — both premises are drawn and nothing else may be added. Now look at what the conclusion claims: all S are P, which would require the part of S outside P to be empty. Inspect that region. Every piece of it has already been shaded, once by each premise. The conclusion is sitting in the diagram without having been drawn. That is the verdict: valid.
Diagram the universal premises before any particular one. A universal shades a region and can decide where an X must go; an X placed first may sit in a region a later shading empties, forcing a guess that the method exists to avoid.