Sheffer stroke

Sheffer stroke
NAND
Venn diagram of Sheffer stroke
Definition
Truth table
Logic gate
Normal forms
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
0-preservingno
1-preservingno
Monotoneno
Affineno
Self-dualno

In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, or alternative denial[1] (since it says in effect that at least one of its operands is false), or NAND ("not and").[1] In digital electronics, it corresponds to the NAND gate. It is named after Henry Maurice Sheffer and written as or as or as or as in Polish notation by Łukasiewicz (but not as ||, often used to represent disjunction).

Its dual is the NOR operator (also known as the Peirce arrow, Quine dagger or Webb operator). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design.

  1. ^ a b Howson, Colin (1997). Logic with trees: an introduction to symbolic logic. London; New York: Routledge. p. 43. ISBN 978-0-415-13342-5.