Logic / Unit 3 Logic 098 worked example, 60 to 90 seconds
Venn Test: Invalid Case
The idea
The same Venn test delivers an invalidity verdict by refusal: both premises are diagrammed, and the region the conclusion needs empty is left partly unshaded.
In practice
Take AAA-2. All P are M. All S are M. So all S are P. Three circles again. Diagram the major premise: all P are M shades the part of P lying outside M. Diagram the minor: all S are M shades the part of S lying outside M. Both premises are now drawn. Look at what the conclusion needs. All S are P requires the whole part of S outside P to be empty. Inspect it. One piece of that region — inside S, inside M, outside P — carries no shading at all. Nothing in either premise ruled it out. The diagram declines to show the conclusion, and that refusal is the verdict. The flaw has a name: both premises relate their terms to M without ever placing S and P in contact, so the middle term is undistributed.
Where people slip
An unshaded region is not a claim that something occupies it. It records that the premises left the question open, which is exactly why the conclusion fails — it asserts more than what was drawn. Reading blankness as evidence of existence turns a correct invalidity verdict into a false one.
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