Routledge Dictionary of Language and Linguistics.pdf

Dictionary of language and linguistics 1068bijectively ( function). Equivalence is both a reflexive relation and a symmetricrelation and a transitive relation. (g) The union set is that set S to which all elementsbelong that are included in at least one of the two original sets A and B (notation:= . The union set corresponds in propositional logic to theinclusive, i.e. to the ‘non-exclusive,’ or, the propositional conjunction of which is true ifone or both statements are true ( disjunction). See the following Venn diagram for(with hachure):For example: let A and B be the sets of abstract words and words ending in -ion inEnglish. The union set is, then, the set of abstract words or words ending in -ion inEnglish (billion, carrion, nation, onion, etc.). (h) The intersection set is the set of thoseelements that are contained both in set A and in set B (notation: A∩B:= xεB}).For example: if A is the set of transitive and B the set of irregular verbs in English, thenthe intersection set of A and B is the set of transitive and irregular verbs in English (bind,eat, come). (i) Difference: the difference is that subset of A that contains exactly the sameelements in A that are not also elements of B (notation: A\B:=. Theunion set of the difference A\B and B\A corresponds in propositional logic to the‘exclusive’ or, the propositional conjunction of which is true only if one of the twostatements linked by or is true (but not if both are true) ( disjunction, exclusivedisjunction). See the following Venn diagram for A\B (with hachure):For example: let A be the set of the transitive verbs in English and B the set of irregularverbs in English. The difference A\B is, then, the set of regular transitive verbs in English(e.g. work). (j) Subset: a set A is a subset of a set B if all elements of A are also elementsof B (notation: .