 A well-known result about classical sentential logic (SL) is that all truth-functions can be expressed in terms of \(\lnot\) and \(\land\) (or of \(\lnot\) and \(\lor\), etc.). A minimal sufficient set of connectives, however, can contain just one connective such as \(\mid\) (“nand,” which is often called, Sheffer’s stroke), or \(\downarrow\) (“nor,” which is Peirce’s joint denial). “Nand” is “not-and,” in other words,  \(A\mid B\) is defined as \(\lnot(A\land B)\), where \(A\), \(B\) range over formulas and \(\lnot\) is negation. Going into the other  direction, if \(\mid\) is a primitive, then \(\lnot A\) is definable as \(A\mid A\), and \(A\land B\) is \((A\mid B)\mid(A\mid B)\).  Although formulas with numerous vertical lines may quickly become  visually confusing and hard to parse, it is straightforward to prove that \(\mid\) alone is sufficiently expressive to define all the truth-functions.