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"
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.