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If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
In many non-theoretical grammars, the terms subject complement (also called a predicative of the subject) and object complement are employed to denote the predicative expressions (predicative complements), such as predicative adjectives and nominals (also called a predicative nominative or predicate nominative), that serve to assign a property to a subject or an object: [3]
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The object complement is bold in the following examples: She painted the barn red. – Adjective as object complement; Here, painted is an attributive ditransitive verb. The direct object is the barn. The object complement construction allows for the combination of the sentences She painted the barn and The barn was painted red. He considers ...
The subject complement is bold in the following examples: The lake was a tranquil pool. – Predicative nominal; Here, was is a copula (a concomitant form of be) that links the subject complement a tranquil pool (which has the head noun pool), to the subject the lake (which has the head noun lake). The lake is tranquil. – Predicative adjective
The complement operation is an involution, meaning it "undoes itself", or the complement of the complement is the original problem. One can generalize this to the complement of a complexity class, called the complement class, which is the set of complements of every problem in the class. [5]
Complement (linguistics), a word or phrase having a particular syntactic role Subject complement, a word or phrase adding to a clause's subject after a linking verb; Phonetic complement; Complementary, a type of opposite in lexical semantics (sometimes called an antonym)
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [ citation needed ] It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.