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Relations and Functions
Relation A 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 ofcodomain. A relation R on set is the subset of A×A. Therefore, R ⊂ A × A. Types of Relations Extreme Relation 1. Empty A relation R in a set A is called empty relation, if no element of A is related to anyelement of A, i.e., R = φ ⊂ A × A. 2. Universal A relation R in a set A is called universal 3. Reflexive A relation R in A is said to be reflexive if aRa for all a∈A 4. Symmetric R is symmetric ifaRb ⇒ bRa, ∀ a, b ∈ A 5. Transitive it is said to be transitive if aRb and bRc ⇒ aRc∀ a, b, c ∈ A ...