8.4 Venn Diagrams

Shading (Venn Symbol)

Represents emptiness; if a section is shaded, nothing exists there.

'X' (Venn Symbol)

Represents existence; means at least one thing exists in that section.

A-Claim (All S are P) Diagram

Shade the part of S that is outside of P (S ∩ ~P); eliminates non-P subjects.

E-Claim (No S are P) Diagram

Shade the overlap/intersection of S and P (S ∩ P); groups never touch.

I-Claim (Some S are P) Diagram

Place an 'X' in the overlap/intersection of S and P.

O-Claim (Some S are not P) Diagram

Place an 'X' in the part of S that is outside of P.

Contradictions (Square of Opposition)

A vs O and E vs I (the diagonals); if one is true, the other MUST be false.

Contraries (The "Ceiling")

Between A and E; they can both be false, but they can NEVER both be true.

Subcontraries (The "Floor")

Between I and O; they can both be true, but they can NEVER both be false.

Contradiction Visual Intuition

One proposition has an 'X' exactly where its contradictory has shading.

A-Claim Exam Tip

Don't shade where things are; shade where they CANNOT be (clearing the room).

Square of Opposition "Ceiling" vs "Floor"

Top (Universal) claims can't both be true; Bottom (Particular) claims can't both be false.