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# 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.

Reference

• 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.

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