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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).
definition: is defined as metalanguage:= means "from now on, ... Sheffer stroke, the sign for the NAND operator (negation of conjunction).
For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: [1] (()) ((())) = where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke).
A CMOS transistor NAND element. V dd denotes positive voltage.. In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringing the output low.
NAND or Sheffer stroke - true when it is not the case that all inputs are true ("not both") NOR or logical nor - true when none of the inputs are true ("neither") XNOR or logical equality - true when both inputs are the same ("equal") An example of a more complicated function is the majority function (of an odd number of inputs).
The vertical bar is a punctuation mark used in computing and mathematics to denote absolute value, logical OR, and pipe commands.
stroke The Sheffer stroke (only used in the second edition of PM) type As in type theory. All objects belong to one of a number of disjoint types. typically Relating to types; for example, "typically ambiguous" means "of ambiguous type". unit A unit class is one that contains exactly one element universal
Similarly, it is sufficient to have only and as logical connectives, or to have only the Sheffer stroke (NAND) or the Peirce arrow (NOR) operator. It is possible to entirely avoid function symbols and constant symbols, rewriting them via predicate symbols in an appropriate way.