Equivalence relation on set is a relation which is reflexive, symmetric and transitive. A relation R, defined in a set A, is said to be an equivalence relation if and only if (i) R is reflexive, that is, aRa for all a ∈ A.(ii) R is symmetric, that is, aRb ⇒ bRa for all a, b ∈ A. (iii) R is transitive, that is aRb and bRc ⇒ aRc for all a, b, c ∈ A. The relation defined by … [Read more...]

## Transitive Relation on Set

What is transitive relation on set?Let A be a set in which the relation R defined.R is said to be transitive, if(a, b) ∈ R and (b, a) ∈ R ⇒ (a, c) ∈ R,That is aRb and bRc ⇒ aRc where a, b, c ∈ A.The relation is said to be non-transitive, if(a, b) ∈ R and (b, c) ∈ R do not imply (a, c ) ∈ R.For example, in the set A of natural numbers if the relation R be defined by ‘x less than … [Read more...]

## Anti-symmetric Relation on Set

What is anti-symmetric relation onset? Let A be a set in which the relation R defined. R is said to be anti-symmetric, if there exist elements, if aRb and bRa ⇒ a = b that is, (a, b) ∈ R and ((b, a) ∈ R ⇒ a = b. A relation R in A is not anti-symmetric, if there exist elements a, b ∈ A, a ≠ b such that aRb and bRa.For example, the relation defined by ‘x is less than or … [Read more...]

## Symmetric Relation on Set

Here we will discuss about the symmetric relation on set.Let A be a set in which the relation R defined. Then R is said to be a symmetric relation, if (a, b) ∈ R ⇒ (b, a) ∈ R, that is, aRb ⇒ bRa for all (a, b) ∈ R.Consider, for example, the set A of natural numbers. If a relation A be defined by “x + y = 5”, then this relation is symmetric in A, for a + b = 5 ⇒ b + a = 5 But … [Read more...]

## Reflexive Relation on Set

Reflexive relation on set is a binary element in which every element is related to itself.Let A be a set and R be the relation defined in it.R is set to be reflexive, if (a, a) ∈ R for all a ∈ A that is, every element of A is R-related to itself, in other words aRa for every a ∈ A.A relation R in a set A is not reflexive if there be at least one element a ∈ A such that (a, a) ∉ … [Read more...]