Editing Propositional formula (section)

=== The stroke (NAND) ===
The binary connective corresponding to NAND is called the [[Sheffer stroke]], and written with a vertical bar | or vertical arrow ↑. The completeness of this connective was noted in ''Principia Mathematica'' (1927:xvii). Since it is complete on its own, all other connectives can be expressed using only the stroke. For example, where the symbol " ≡ " represents ''logical equivalence'':
: ~p ≡ p|p
: p → q ≡ p|~q
: p &or; q ≡ ~p|~q
: p & q ≡ ~(p|q)
In particular, the zero-ary connectives <math>\top</math> (representing truth) and <math>\bot</math> (representing falsity) can be expressed using the stroke:
: <math>\top \equiv (a|(a|a))</math>
: <math>\bot \equiv (\top | \top)</math>