Question

Give detailed Conception of : Types of Relations.

Answer 1

@terenzreignz @nader1 @waterineyes @Eyad

Answer 2

Equivalence Relation's got to be one of the first answers... unless you had something else in mind?

Answer 3

Void relation

Answer 4

ya ok please tell about it.

Answer 5

Relation is a subset of Cartesian product of two sets. We have seen that power set of Cartesian product “ A×B ” is a set of all possible relations among the elements of sets “A” and “B”. In the case of “relation on A”, the power set of Cartesian product “ A×A ” is a set of all possible relations among the elements of set “A”.

One of the subsets of the power set is empty set or void set. This subset without any element is called the void relation.

R=φ={}

Answer 6

Beautiful ^

Answer 7

you can many type Universal relation

Answer 8

*have many type

Answer 9

Identity relation it is a type

Answer 10

In an identity relation "R", every element of the set “A” is related to itself only.
Note the conditions conveyed through words “every” and “only”. The word “every” conveys that identity relation consists of ordered pairs of element with itself - all of them. The word “only” conveys that this relation does not consist of any other combination.

Consider a set A={1,2,3}. Then, its identity relation is :

R={(1,1),(2,2),(3,3)}

It is evident that a set has only one such relation. This relation, as we can see, identifies the set - as it identifies each elements of the set, which are related to itself. By looking at the relation, we can identify the set itself. For this reason, the name of this relation is identity relation. In set builder form, we express an identity relation as

R={(x,x):for allx∈A}

The qualification of the relation is that first and second element of the ordered pair is same element, which belongs to set A.

The followings are not an identity relation :

R1={(1,1),(2,2)}

R2={(1,1),(2,2),(3,3),(1,2),(1,3)}

First one is not an identity relation as it does not include the pairing of remaining element “3”. Second is not an identity relation, because there are other combinations of pairs in the relation.