Sheffer stroke

The Sheffer stroke, usually written ↑, is the binary logical connective that is false only when both inputs are true. It represents NAND and can express every truth-functional connective by itself.

NAND gate: A digital logic gate whose output is false only when all inputs are true. The electronic gate implements the same NAND operation as the Sheffer stroke.
Propositional calculus: A formal system for reasoning with propositions and truth-functional connectives. The Sheffer stroke is studied as a connective within this logical system.
Henry M. Sheffer: An American logician who introduced the stroke notation for a single connective sufficient to express propositional logic. His 1913 work established the connective’s place in modern logic.
Peirce arrow: The NOR connective, usually written ↓, which is true only when both inputs are false. Like the Sheffer stroke, it is functionally complete, but it negates disjunction instead of conjunction.
Truth table: A table that lists a logical expression’s output for every possible assignment of its inputs. Its four rows give the Sheffer stroke’s complete truth condition.
Logical connective: An operation that combines or modifies propositions to form new propositions. The Sheffer stroke is one binary connective in this broader family.
Principia Mathematica: A three-volume work by Bertrand Russell and Alfred North Whitehead seeking to derive mathematics from symbolic logic. Sheffer demonstrated that its primitive connectives could be reduced to one stroke.
Logical equivalence: A relation holding between propositions that have the same truth value under every interpretation. The stroke’s alternative notation does not change its truth-functional meaning.
Boolean function: A function that maps Boolean inputs to a Boolean output. The Sheffer stroke is a two-input Boolean function with a distinctive universal property.
Material implication: The truth-functional connective that is false only when its antecedent is true and its consequent false. NAND can define implication, showing its reach beyond negation and conjunction.

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