Logic / Unit 3 Logic 097 worked example, 60 to 90 seconds
Venn Test: Valid Case
The idea
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.
In practice
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.
Where people slip
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.
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