A binary relation is a collection of Sets between two Sets ‘M’ and ‘N’ which is the subset of M * N, or we can say that it is a Set of Ordered Pair m, n Є M*N. Here set of ‘M’ and ‘N’ are known as Domain. |

**Binary relation can be defined as a relation on Set P which is a set of Ordered Pair of elements or we can say that binary relation is a sub set of Cartesian product that is (P2 = P x P).**Binary relation among two Sets P and Q is a subset of P x Q. Binary relation is also known as dyadic relation and 2 – place relation. For example: It is a relation between set of prime Numbers Q and set of integers R in such a way that every Prime number Q is related with every Integer R which is multiple of Q. Now we will see some Binary Relations properties. Properties of binary relations are mentioned below:

Reflexive relation

Irreflexive relation

Symmetric relation

Transitive relation

Reflexive relation

Irreflexive relation

Symmetric relation

Transitive relation

Let’s have small introduction about above mentioned properties of binary relation.

Reflexive relation: Reflexive relation can be defined as a relation R on set U which is said to be reflexive relation if and only if < u, u > є R for each element of u of set U. In other words we can say if element of set U are related to itself. For example: ‘b’ is related to itself.

Irreflexive relation: it is defined as a relation R on a set U which is said to be irreflexive relation if and only if < u, u > does not belong to relation R for each element of u of set U.

Symmetric relation: It is defined as a relation R on set U which is said to be symmetric relation if and only if for any u and v element in U, whenever < u, v > є R, <v, u> є R.

Transitive relation: It is defined as relation R on a set U which is said to be transitive relation if and only if for any u, v and w in set U, whenever < u, v > є R, and < v, w > є R, < u, w > є R relation. This is all about the properties of binary relations.

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