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)