# truth-function

- 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. 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.

*Philosophy dictionary.
Academic.
2011.*

### Look at other dictionaries:

**Truth function**— Truth functional redirects here, for the truth functional conditional, see Material conditional. In mathematical logic, a truth function is a function from a set of truth values to truth values. Classically the domain and range of a truth… … Wikipedia**truth function**— noun (logic) A function that determines whether or not a complex sentence is true depending on the truth values of the component parts of the sentence • • • Main Entry: ↑truth … Useful english dictionary**truth-function**— truth functional, adj. truth functionally, adv. /troohth fungk sheuhn/, n. Logic. a statement so constructed from other statements that its truth value depends on the truth values of the other statements rather than on their meanings. * * * … Universalium**truth-function**— ˈ ̷ ̷ˌ ̷ ̷ ̷ ̷ noun Etymology: translation of German wahrheitsfunktion : a sentential or propositional function whose truth value depends only on the truth values of its arguments • truth functional (ˈ) ̷ ̷| ̷ ̷( ̷ ̷) ̷ ̷ adjective • truth… … Useful english dictionary**truth function**— noun A Boolean function whose value is interpreted as truth or falsity … Wiktionary**truth functions**— truth function … Philosophy dictionary**truth-functional**— truth function … Philosophy dictionary**truth-functions**— truth function … Philosophy dictionary**Function (mathematics)**— f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia**Truth table**— A truth table is a mathematical table used in logic specifically in connection with Boolean algebra, boolean functions, and propositional calculus to compute the functional values of logical expressions on each of their functional arguments, that … Wikipedia