John Venn gave the four forms a picture. Draw two overlapping circles, the subject class S on the left and the predicate class P on the right. They make four regions: 1 (S only), 2 (both), 3 (P only) and 4 (outside both).
Key idea
Shading a region means it is empty. An X in a region means at least one thing is there. A and E shade; I and O put an X.
| Form | What it says | Diagram |
|---|---|---|
| All S are P | no S outside P | shade region 1 |
| No S are P | no S inside P | shade region 2 |
| Some S are P | something is in S and P | X in region 2 |
| Some S are not P | something is in S but not P | X in region 1 |
Why it works
Each form talks about exactly one region. "All S are P" is the same claim as "there is nothing that is S but not P", so its region, 1, is empty. "Some S are P" is the claim "there is something that is both", so region 2 gets an X. Turning every statement into a claim about which regions are empty or occupied is what makes pictures able to test reasoning later.
Worked example
Worked example: Reading a diagram
With S = runners and P = poets, region 1 is shaded and nothing else is marked. Which statement is that?
- Region 1 is runners who are not poets. Shading says there are none.
- "No runners are outside the poets" is the same as "All runners are poets".
Answer: All runners are poets
Common mistake
Shading the region the statement talks about instead of the region it says is empty. For "All S are P", people often shade the overlap because "S are P" sounds like the overlap. But A says the part of S outside P is empty, so shade region 1. Check: after shading, every S left in the picture should be inside P.