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     TFT
T F | T T F     TTF
F T | T F T     FTT
F F | T F F     FTF

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 | FT | TFT
F | TF | FTF

For another example, here is the implication (conditional)
P Q  P->Q  | (P|(P|Q))
T T  TTT   |  TT  TF T
T F  TFF   |  TF  TT F
F T  FTT   |  FT  FT T
F F  FTF   |  FT  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

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