A truth function of a number of propositions or sentences is a function of them that has a definite truth-value, dependent only on the truth-values of the constituents. Thus (p & q) is a combination whose truth-value is true when p is true and q is true, and false otherwise. ¬p is a truth function of p, false when p is true and true when p is false. The way in which the value of the whole is determined by the combinations of values of constituents is presented in a truth table.
![truth function](Images/oree/doc/10.1093/acref/9780198735304.001.0001/acref-9780198735304-graphic-015-full.gif)
The propositional calculus is the standard treatment of truth-functional combinations. Its constants, &, ∨, ¬, → and ↔, are all truth functors, i.e. expressions standing for truth functions.