Sheffer stroke
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Sheffer stroke
The Sheffer stroke (also called NAND) is a logical operation that returns true unless both propositions are true. It is functionally complete, meaning all other logical operations can be built from it.
Symbols
- p ↑ q (mathematical notation)
- p NAND q (common name)
- NOT (p ∧ q) (definition)
Definition
The Sheffer stroke produces the negation of conjunction.
Truth Table
| p | q | p ↑ q |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
Examples
- If p = "The switch is on" and q = "The light is on",
then p ↑ q = "It is not the case that the switch and the light are both on".
- In digital logic, NAND gates are fundamental building blocks for circuits.
- In Python:
not (p and q) - In Java:
!(p && q)