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The stroke is named after Henry Maurice Sheffer, who in 1913 published a paper in the Transactions of the American Mathematical Society [10] providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by Huntington employing the familiar operators of propositional logic (AND, OR, NOT).
It is one of 25 candidate axioms for this property identified by Stephen Wolfram, by enumerating the Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models with four or fewer variables, and was first proven equivalent by William McCune, Branden Fitelson, and Larry Wos.
Sheffer stroke: Is the contemporary logical NAND (NOT-AND), i.e., "incompatibility", meaning: "Given two propositions p and q, then ' p | q ' means "proposition p is incompatible with proposition q", i.e., if both propositions p and q evaluate as true, then and only then p | q evaluates as false." After section 8 the Sheffer stroke sees no usage.
Because Sheffer's stroke (also known as NAND operator) is functionally complete, it can be used to create an entire formulation of propositional calculus. NAND formulations use a rule of inference called Nicod's modus ponens:
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
The result was the minimum wage racing past $6, $7, and even $8 for the first time in history with the stroke of a pen. Lionel Green / Staff / Archive Photos / Getty Images CC. 1951.
Shohei Ohtani was back on the mound, throwing his first bullpen session in spring training since 2023, surrounded by more than 1,000 fans.
The vertical bar is a punctuation mark used in computing and mathematics to denote absolute value, logical OR, and pipe commands.