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In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
Here is an example of an argument that fits the form conjunction introduction: Bob likes apples. Bob likes oranges. Therefore, Bob likes apples and Bob likes oranges. Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.
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]
A symbol or word used in logic to connect propositions or sentences, forming more complex expressions that convey relationships such as conjunction, disjunction, and negation. logical consequence A relationship between statements where the truth of one or more premises necessitates the truth of a conclusion, based on the logical structure of ...
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 terminals, disjoint from V, which make up the actual content of the sentence. The set of terminals is the alphabet of the language defined by the grammar G.
For example, in the sentence "She likes apples and oranges", the coordinator and connects two elements (apples and oranges) of equal importance. In contrast, in the sentence "She knew that he was lying", the subordinator that marks the clause "he was lying" as subordinate to the main clause "She knew".
In linguistics (especially generative grammar), a complementizer or complementiser (glossing abbreviation: comp) is a functional category (part of speech) that includes those words that can be used to turn a clause into the subject or object of a sentence. For example, the word that may be called a complementizer in English sentences like Mary ...
Because the word there can also be a deictic adverb (meaning "at/to that place"), a sentence like There is a river could have either of two meanings: "a river exists" (with there as a pronoun), and "a river is in that place" (with there as an adverb).