Peirce arrow

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Peirce arrow

The Peirce arrow (also called NOR) is a logical operation that returns true only when both propositions are false. It is functionally complete, meaning all other logical operations can be expressed in terms of it.

Symbols

  • p ↓ q (mathematical notation)
  • p NOR q (common name)
  • ¬(p ∨ q) (definition)

Definition

The Peirce arrow produces the negation of disjunction.

Truth Table

p q p ↓ q
T T F
T F F
F T F
F F T

Examples

  • If p = "I will travel" and q = "I will study",
 then p ↓ q = "It is not the case that I will travel or study" (meaning: I do neither).
  • In Python: not (p or q)
  • In Java: !(p || q)