Conjunction Reduction
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Conjunction Reduction
Conjunction may refer to: * Conjunction (grammar), a part of speech * Logical conjunction, a mathematical operator ** Conjunction introduction, a rule of inference of propositional logic * Conjunction (astronomy), in which two astronomical bodies appear close together in the sky * Conjunction (astrology), astrological aspect in horoscopic astrology * ''Conjunctions (journal), Conjunctions'', an American literary journal {{disambig ...
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Conjunction (grammar)
In grammar, a conjunction (list of glossing abbreviations, abbreviated or ) is a part of speech that connects words, phrases, or clauses that are called the conjuncts of the conjunctions. That definition may overlap with that of other parts of speech and so what constitutes a "conjunction" must be defined for each language. In English, a given word may have several word sense, senses and be either a preposition or a conjunction, depending on the syntax of the sentence. For example, ''after'' is a preposition in "he left after the fight" but is a conjunction in "he left after they fought". In general, a conjunction is an invariable (non-inflection, inflected) grammatical particle that may or may not stand between the items conjoined. The definition of conjunction may also be extended to idiomatic phrases that behave as a unit with the same function, "as well as", "provided that". A simple literary example of a conjunction is "the truth of nature, ''and'' the power of giving inte ...
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Logical Conjunction
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 ...
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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 ...
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Conjunction (astronomy)
In astronomy, a conjunction occurs when two astronomical objects or spacecraft have either the same right ascension or the same ecliptic longitude, usually as observed from Earth. When two objects always appear close to the ecliptic—such as two planets, the Moon and a planet, or the Sun and a planet—this fact implies an apparent close approach between the objects as seen in the sky. A related word, ''appulse'', is the minimum apparent separation in the sky of two astronomical objects. Conjunctions involve either two objects in the Solar System or one object in the Solar System and a more distant object, such as a star. A conjunction is an apparent phenomenon caused by the observer's perspective: the two objects involved are not actually close to one another in space. Conjunctions between two bright objects close to the ecliptic, such as two bright planets, can be seen with the naked eye. The astronomical symbol for conjunction is (Unicode U+260C ☌). The conjunction ...
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Conjunction (astrology)
In astrology, an aspect is an angle that planets make to each other in the Horoscope; as well as to the Ascendant, Midheaven, Descendant, Lower Midheaven, and other points of astrological interest. As viewed from Earth, aspects are measured by the angular distance in degrees and minutes of ecliptic longitude between two points. According to astrological tradition, they indicate the timing of transitions and developmental changes in the lives of people and affairs relative to the Earth. For example, if an astrologer creates a Horoscope that shows the apparent positions of the celestial bodies at the time of a person's birth (Natal Chart), and the angular distance between Mars and Venus is 92° ecliptic longitude, the chart is said to have the aspect "Venus Square Mars" with an orb of 2° (i.e., it is 2° away from being an exact Square; a Square being a 90° aspect). The more exact an aspect, the stronger or more dominant it is said to be in shaping character or manifesting ...
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