Both Peirce in 1880 and the American logician H. M. Sheffer in 1913 realized that the truth functions of elementary logic could all be defined from a single function. Defining p / q to mean not both p and q, p / p is equivalent to not-p, (p / q)/ (p / q) means p ∨q, and so on. A functionally complete system can also be built from a single sign for the function that is true when p is false and q is false.