Transcription of RELATIONS AND FUNCTIONS - NCERT
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RELATIONS AND FUNCTIONS - NCERT
Relation R from a non-empty set A to a non empty set B is a subset of the Cartesianproduct A B. The set of all first elements of the ordered pairs in a relation R from aset A to a set B is called the domain of the relation R. The set of all second elements ina relation R from a set A to a set B is called the range of the relation R. The whole setB is called the codomain of the relation R. Note that range is always a subset of RelationsA relation R in a set A is subset of A A. Thus empty set and A A are two extremerelations.(i) A relation R in a set A is called empty relation, if no element of A is related to anyelement of A, , R = A A.(ii) A relation R in a set A is called universal relation, if each element of A is relatedto every element of A, , R = A A.
RELATIONS AND FUNCTIONS 3 (v) Given a binary operation * : A × A → A, with the identity element e in A, an element a ∈ A, is said to be invertible with respect to the operation *, if there exists an element b in A such that a * b = e = b * a and b is called the inverse of a and is denoted by a–1. 1.2 Solved Examples Short Answer (S.A.)
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