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• Truth_function abstract "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 function are {truth, falsehood}, but they may have any number of truth values, including an infinity of these.A logical connective is truth-functional if the truth-value of a compound sentence is a function of the truth-value of its sub-sentences. A class of connectives is truth-functional if each of its members is. For example, the connective \"and\" is truth-functional since a sentence like \"Apples are fruits and carrots are vegetables\" is true if, and only if each of its sub-sentences \"apples are fruits\" and \"carrots are vegetables\" is true, and it is false otherwise. Some connectives of a natural language, such as English, are not truth-functional.Connectives of the form \"x believes that ...\" are typical examples of connectives that are not truth-functional. If e.g. Mary mistakenly believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese, then the sentence\"Mary believes that Al Gore was President of the USA on April 20, 2000\"is true while\"Mary believes that the moon is made of green cheese\"is false. In both cases, each component sentence (i.e. \"Al Gore was president of the USA on April 20, 2000\" and \"the moon is made of green cheese\") is false, but each compound sentence formed by prefixing the phrase \"Mary believes that\" differs in truth-value. That is, the truth-value of a sentence of the form \"Mary believes that...\" is not determined solely by the truth-value of its component sentence, and hence the (unary) connective (or simply operator since it is unary) is non-truth-functional.The class of classical logic connectives (e.g. &, →) used in the construction of formulas is truth-functional. Their values for various truth-values as argument are usually given by truth tables. Truth-functional propositional calculus is a formal system whose formulas may be interpreted as either true or false.".
• Truth_function thumbnail Venn0000.svg?width=300.
• Truth_function wikiPageID "604707".
• Truth_function wikiPageLength "21689".
• Truth_function wikiPageOutDegree "89".
• Truth_function wikiPageRevisionID "666224253".
• Truth_function wikiPageWikiLink Absorption_law.
• Truth_function wikiPageWikiLink Affine_transformation.
• Truth_function wikiPageWikiLink Alfred_North_Whitehead.
• Truth_function wikiPageWikiLink Alonzo_Church.
• Truth_function wikiPageWikiLink Apollo_Guidance_Computer.
• Truth_function wikiPageWikiLink Arity.
• Truth_function wikiPageWikiLink Associative_property.
• Truth_function wikiPageWikiLink Bertrand_Russell.
• Truth_function wikiPageWikiLink Binary_function.
• Truth_function wikiPageWikiLink Binary_operation.
• Truth_function wikiPageWikiLink Bitwise_operation.
• Truth_function wikiPageWikiLink Boolean-valued_function.
• Truth_function wikiPageWikiLink Boolean_algebra.
• Truth_function wikiPageWikiLink Boolean_domain.
• Truth_function wikiPageWikiLink Boolean_function.
• Truth_function wikiPageWikiLink Category:Mathematical_logic.
• Truth_function wikiPageWikiLink Category:Truth.
• Truth_function wikiPageWikiLink Classical_logic.
• Truth_function wikiPageWikiLink Commutative_property.
• Truth_function wikiPageWikiLink Degeneracy_(mathematics).
• Truth_function wikiPageWikiLink Digital_electronics.
• Truth_function wikiPageWikiLink Distributive_property.
• Truth_function wikiPageWikiLink Domain_of_a_function.
• Truth_function wikiPageWikiLink Dynamic_random-access_memory.
• Truth_function wikiPageWikiLink False_(logic).
• Truth_function wikiPageWikiLink Formal_system.
• Truth_function wikiPageWikiLink Function_(mathematics).
• Truth_function wikiPageWikiLink Function_composition.
• Truth_function wikiPageWikiLink Functional_completeness.
• Truth_function wikiPageWikiLink Idempotence.
• Truth_function wikiPageWikiLink If_and_only_if.
• Truth_function wikiPageWikiLink Inclusion–exclusion_principle.
• Truth_function wikiPageWikiLink Józef_Maria_Bocheński.
• Truth_function wikiPageWikiLink List_of_Boolean_algebra_topics.
• Truth_function wikiPageWikiLink Logic_gate.
• Truth_function wikiPageWikiLink Logical_NOR.
• Truth_function wikiPageWikiLink Logical_conjunction.
• Truth_function wikiPageWikiLink Logical_connective.
• Truth_function wikiPageWikiLink Logical_constant.
• Truth_function wikiPageWikiLink Logical_equivalence.
• Truth_function wikiPageWikiLink Logical_truth.
• Truth_function wikiPageWikiLink Ludwig_Wittgenstein.
• Truth_function wikiPageWikiLink Material_conditional.
• Truth_function wikiPageWikiLink Mathematical_logic.
• Truth_function wikiPageWikiLink Maximal_element.
• Truth_function wikiPageWikiLink Modal_operator.
• Truth_function wikiPageWikiLink Monotonic_function.
• Truth_function wikiPageWikiLink Negation.
• Truth_function wikiPageWikiLink Partition_of_a_set.
• Truth_function wikiPageWikiLink Principia_Mathematica.
• Truth_function wikiPageWikiLink Principle_of_compositionality.
• Truth_function wikiPageWikiLink Propositional_calculus.
• Truth_function wikiPageWikiLink Range_(mathematics).
• Truth_function wikiPageWikiLink Set_(mathematics).
• Truth_function wikiPageWikiLink Sheffer_stroke.
• Truth_function wikiPageWikiLink Ternary_operation.
• Truth_function wikiPageWikiLink Tractatus_Logico-Philosophicus.
• Truth_function wikiPageWikiLink Truth.
• Truth_function wikiPageWikiLink Truth_function.
• Truth_function wikiPageWikiLink Truth_table.
• Truth_function wikiPageWikiLink Truth_value.
• Truth_function wikiPageWikiLink Turing_completeness.
• Truth_function wikiPageWikiLink Unary_operation.
• Truth_function wikiPageWikiLink Validity.
• Truth_function wikiPageWikiLinkText "Functional completeness in truth function".
• Truth_function wikiPageWikiLinkText "More information".
• Truth_function wikiPageWikiLinkText "Truth function in computer science".
• Truth_function wikiPageWikiLinkText "Truth function".
• Truth_function wikiPageWikiLinkText "non-truth-functional".
• Truth_function wikiPageWikiLinkText "truth function".
• Truth_function wikiPageWikiLinkText "truth-functional".
• Truth_function also "/False".
• Truth_function also "/True".
• Truth_function equivalents "Apq".
• Truth_function equivalents "Bpq".
• Truth_function equivalents "Cpq".
• Truth_function equivalents "Dpq".
• Truth_function equivalents "Epq".
• Truth_function equivalents "Fpq".
• Truth_function equivalents "Gpq".
• Truth_function equivalents "Hpq".
• Truth_function equivalents "Ipq".
• Truth_function equivalents "Jpq".
• Truth_function equivalents "Kpq".
• Truth_function equivalents "Lpq".
• Truth_function equivalents "Mpq".
• Truth_function equivalents "Np".
• Truth_function equivalents "Nq".
• Truth_function equivalents "Opq".
• Truth_function equivalents "P ¬P".
• Truth_function equivalents "P ¬Q".
• Truth_function equivalents "P ¬Q".
• Truth_function equivalents "P ↑ ¬Q".
• Truth_function equivalents "P → ¬Q".

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