Venn Diagram Key — Categorical Logic

Quick-reference for reading two-circle Venn diagrams in categorical logic.

Convention: Shading = region is empty (no members). X = at least one member exists there.

Two-Circle Reading Key

Diagram	Shaded / Marked Region	Statement
S-only crescent shaded	Left crescent (in S, not P)	All S are P
P-only crescent shaded	Right crescent (in P, not S)	All P are S
Intersection shaded	Middle overlap (S ∩ P)	No S are P
X in intersection	Middle overlap (S ∩ P)	Some S are P
X in S-only crescent	Left crescent (in S, not P)	Some S are not P

Diagram

graph LR
    A["S-only crescent<br/>(shaded)"] --> B["All S are P"]
    C["P-only crescent<br/>(shaded)"] --> D["All P are S"]
    E["Intersection<br/>(shaded)"] --> F["No S are P"]
    G["X in intersection"] --> H["Some S are P"]
    I["X in S-only crescent"] --> J["Some S are not P"]

Related Concepts

• CategoricalStatements — A/E/I/O proposition types
• ImmediateInference — conversion, contraposition, obversion
• Syllogism — three-circle Venn diagrams for testing validity