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For example, after is a preposition in "he left after the fight" but a conjunction in "he left after they fought". In general, a conjunction is an invariant (non-inflecting) grammatical particle that stands between conjuncts. A conjunction may be placed at the beginning of a sentence, [1] but some superstition about the practice persists. [2]
Logical conjunction. In logic, mathematics and linguistics, and ( ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as [1] or or (prefix) or or [2] in which is the most modern and widely used. The and of a set of operands is true if and only if all of its ...
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) [1][2][3] 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 is true, and the proposition is true, then the ...
A conjunctive grammar is defined by the 4- tuple where. is called a nonterminal symbol or a variable. Each variable represents a different type of phrase or clause in the sentence. Variables are also sometimes called syntactic categories. Σ is a finite set of terminal s, disjoint from V, which make up the actual content of the sentence. The ...
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
and expressed as truth-functional tautologies or theorems of propositional logic: (), ().where and are propositions expressed in some formal system.. The generalized De Morgan’s laws provide an equivalence for negating a conjunction or disjunction involving multiple terms.
A conjunct is one of the terms that are conjoined in a conjoining construction. Conjuncts are conjoined by means of a conjunction, which can be coordinating, subordinating or correlative. Conjuncts can be words, phrases, clauses, or full sentences. [Gretchen and her daughter] bought [motor oil, spark plugs, and dynamite].
Commutativity of conjunction. In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic. It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting ...