In

propositional logic, the Sheffer stroke is an

operator, or

connective, which is

semantically complete.
Each

connective in

Logic has an associated

truth table. These connectives can be combined to create new

truth tables. The Sheffer stroke is a

connective that allows one to create a

formula for any truth table using this

operator alone.

The Sheffer stroke is analagous to a NAND operation, and is

symbolized with the '|' char.

P Q | ~(P^Q) | (P|Q)
-----------------
T T | **F** T T T**F**T
T F | **T** T F T**T**F
F T | **T** F T F**T**T
F F | **T** F F F**T**F

From this figure it can be seen that a Sheffer stroke is only

false if both of its

operands are true.

By combining the Sheffer stroke with itself, any truth table can be contrived.

Here is the

truth table for the

negation operator:

P | ~P | (P|P)
-------
T | **F**T | T**F**T
F | **T**F | F**T**F

For another example, here is the

implication (conditional)

P Q P->Q | (P|(P|Q))
-----------------
T T T**T**T | T**T** TF T
T F T**F**F | T**F** TT F
F T F**T**T | F**T** FT T
F F F**T**F | F**T** FT F

Here is AND

P^Q (P|Q)|(P|Q)

Here is OR

PvQ (P|P)|(Q|Q)

For the same reason that the Sheffer stroke may be used to create any truth table, any

logical circuit consisting of AND, OR GATES and

inverters can be created using only

NAND Gates