Types of relations are always to be the properties of interaction, which are reflexive, symmetric, transitive, antisymmetric and are to be understood in the below topics. A relation from your set A to your set B is usually a subset of A * B. A relation on a set A is usually a subset of A *A. If a relation A is supposed to have n elements, then a relation on A has between 0 and n$^2$ elements and there are 2$^{n^2}$ possible relations on A. If f is usually a function from A to A, then {(a,b) | a $\in$ A, f(a) = b} is a relation on A. Learn the several types of sets relation in this article and understand these kinds in depth from the proper explanation furnished.

Properties of Relations

Some of the important properties of relations are given below.

A relation R on a set A is reflexive if for all x, ((x,x) $\in$ R)
Examples : =, $\leq$, $\geq$

A relation R on a set A is symmetric if for all x, y ((x,y) $\in$ R $\rightarrow$ (y,x) $\in$ R)
Examples : =, $\neq$

A relation R on a set A is antisymmetric if for all x,y ((x,y) $\in$
R $\rightarrow$ ( x = y V (y,x) $\neq$ R))
Examples : =, <, $\leq$, $\geq$, >

A relation R on a set A is transitive if for all x, y and z (((x;y) $\in$ R ^ (y,z) $\in$ R) $\rightarrow$ (x, z) $\in$ R)
Examples : =, $\leq$, $\geq$, <, >

Different Standard Relations

A great equivalence relation is usually a relation which is reflexive, symmetric along with transitive. For every equivalence relation you will find there's natural way to divide the set on what it is identified into mutually exclusive subsets that happen to be called equivalence lessons.

We write[[x]] for the set of all y in ways that <x, y> $\in$ R.

Example: The relations “has identical hair color as” in the set of
everyone is equivalence relations. The equivalence classes within the relation “has identical hair color as” include the set of blond individuals, the set connected with red-haired people, and so on.

Possible types of Set relations

Some of the very important possible types of set relations are discussed below in the following points.

1. On the list of constructive integers Z+, this relative “a divides b” will be
reflexive
not necessarily symmetric
transitive

2. On the list of constructive integers Z+, this relative "a is
not necessarily reflexive
not necessarily symmetric
transitive

3. On the list of triangles, the relation “similar to” will be
reflexive
symmetric
transitive

4. On the list of lines in a plane, this relative “parallel to” will be
reflexive
symmetric
transitive

5. On the list of lines in a plane, this relation “perpendicular to” will be
not necessarily reflexive
symmetric
not necessarily transitive

6.  On the widespread list of sets, the relation  “subset of” will be
reflexive
not necessarily symmetric
transitive

7.  On the widespread list of sets, this relation “subset of” is surely an
antisymmetric relative.

8. On the list of integers, this relation “congruence” is surely an equivalence relation.