What is a relation?
A relation R defined in a set A is a subset of A ×A
Empty Relation: A relation R in a set A is called empty relation, if no element of A is related to any element of A, i.e., R = = A × A.
Universal Relation: A relation R in a set A is called universal relation, if each element of A is related to every element of A, i.e., R = A × A.
Both the empty relation and the universal relation are also called trivial relations.
Reflexive relation: A relation in a set A is said to be reflexive if and only if (a, a) ∈ R for every a ∈ set A.
Symmetric Relation: A relation R on a set A is said to be symmetric if and only if (a, b) ∈ R implies that (b, a) is also belonging to R where a, b ∈ A.
Transitive relation: A relation R on a set A is said to be transitive if and only if (a, b) ∈R and (b, c) ∈R implies that (a, c) is also belonging to R where a, b, c ∈ A.
Equivalence relation: A relation R on a set A is said to be equivalence relation if and only if it is reflexive, symmetric and transitive.
