Encyclopedia > Sheffer stroke

  Article Content

Sheffer stroke

The Sheffer stroke, also known as the NAND operation, is a logical operator with the following meaning: p NAND q is true if and only if not both p and q are true. It is named for Henry M. Sheffer, who proved that all the usual operators of logical calculus (not, and, or, implies) could be expressed in terms of it:
"not p" is equivalent to "p NAND p"
"p and q" is equivalent to "(p NAND q) NAND (p NAND q)"
"p or q" is equivalent to "(p NAND p) NAND (q NAND q)"
"p implies q" is equivalent to "(p NAND q) NAND p"

This leads to an alternative axiom system for boolean algebras that needs only one operation.

There is another logical operator which is able to express all the others: NOR.


  • A set of five independent postulates for Boolean algebras, with application to logical constants. Transactions of the American Mathematical Soc. 14 (1913), pp. 481-488.

See Also

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Ocean Beach, New York

... village has a total area of 0.4 km² (0.1 mi²). 0.4 km² (0.1 mi²) of it is land and none of the area is covered with water. Demographics As of th ...

This page was created in 23.8 ms