There are various types of relations:Let A be a non-empty set. Then, a relation R on A is said to be• Reflexive if (a, a) ∈ R for each a ∈ A, i.e., if a R a for each a ∈ A. For example, the relation “is as strong as” is reflexive since every member of a particular set will be as strong as himself, but the relation 'isthe mother of 'is not reflexive as a person cannot be his/her own mother.• Symmetric if (a, b) ∈ R ⇒ (b, a) ∈ R for all a, b ∈ A, i.e., if a R b ⇒ b R a for all a, b ∈ A. For example, the relation “weighs the same as” is symmetric as if x weighs same as y. Then y weighs same as x, but the relation “is less than” is not symmetric as: if x is less than y, then y is not less than x.• Transitive if (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R for all a, b, c ∈ A, i.e., if a R b and b R c then a R c. For example, the relation equals tois a transitive relation for if x = y and y = z, then x = z, but the relation “is perpendicular to” on a set of coplanar lines is not transitive for if line a is perpendicular to line b and line b is perpendicular to line c, then line a is not perpendicular to line c. • Equivalence: A relation R on a set A is said to be an equivalence relation if it is reflexive, symmetric and transitive.For example, (i) “Equality” is an equivalence relation because • x = x • x = y ⇒ y = x • x = y, y = z ⇒ x = z.(ii) “Is parallel to” on a set A of coplanar lines is an equivalence relation since: for all the lines a, b, c ∈ A. • a || a • a || b ⇒ b || a • a || b, b || c ⇒ a || c.