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And (logic)
In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents this operator is typically written as \wedge or . A \land B is true if and only if A is true and B is true, otherwise it is false. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English "and". * In programming languages, the short-circuit and control structure. * In set theory, intersection. * In lattice theory, logical conjunction (greatest lower bound). * In predicate logic, universal quantification. Notation And is usually denoted by an infix operator: in mathematics and logic, it is denoted by \wedge, or ; in electronics, ; and in programming languages, &, &&, or and. In Jan Łuk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venn 0000 0001
Venn is a surname and a given name. It may refer to: Given name * Venn Eyre (died 1777), Archdeacon of Carlisle, Cumbria, England * Venn Pilcher (1879–1961), Anglican bishop, writer, and translator of hymns * Venn Young (1929–1993), New Zealand politician Surname * Albert Venn (1867–1908), American lacrosse player * Anne Venn (1620s–1654), English religious radical and diarist * Blair Venn, Australian actor * Charles Venn (born 1973), British actor * Harry Venn (1844–1908), Australian politician * Henry Venn (Church Missionary Society) the younger (1796-1873), secretary of the Church Missionary Society, grandson of Henry Venn * Henry Venn (Clapham Sect) the elder (1725–1797), English evangelical minister * Horace Venn (1892–1953), English cricketer * John Venn (1834–1923), British logician and the inventor of Venn diagrams, son of Henry Venn the younger * John Venn (academic) (died 1687), English academic administrator * John Venn (politician) (1586–1650), Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Quantification
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable. It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("", "", or sometimes by "" alone). Universal quantification is distinct from ''existential'' quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is encoded as in Unicode, and as \forall in LaTeX and relate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjunction Introduction
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition P is true, and the proposition Q is true, then the logical conjunction of the two propositions P and Q is true. For example, if it is true that "it is raining", and it is true that "the cat is inside", then it is true that "it is raining and the cat is inside". The rule can be stated: :\frac where the rule is that wherever an instance of "P" and "Q" appear on lines of a proof, a "P \land Q" can be placed on a subsequent line. Formal notation The ''conjunction introduction'' rule may be written in sequent notation: : P, Q \vdash P \land Q where P and Q are propositions expressed in some formal system, and \vdash is a metalogical symbol meaning that P \land Q is a syntactic consequence if P an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is generally credited with inventing and popularizing the truth table ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
