Universal Relation

Universal relation is a relation on set A when A X A $\subseteq $ A X A. In other words, universal-relation is the relation if each element of set A is related to every element of A.
For example : Relation on the set A = {1,2,3,4,5,6} by
R = {(a,b) $\in$ R : |a -b|$\geq $0}
We observe that |a -b|$\geq $0 for all a, b $\in$ A
$\Rightarrow $(a,b)$\in$ R for all (a,b) $\in$ A X A
$\Rightarrow $ each element of set A is related to every element of set A.
$\Rightarrow $ R = A X A
$\Rightarrow $ R is a universal relation on set A.
Note : It is to note here that the void relation and the universal relation on a set A are respectively the smallest and the largest relations on set A.
Both the void and universal relation are sometimes called trivial relations.

Examples on Universal Relation

Example : 1 Let A be the set of all students of a boys school. Show that the relation R on A given by R = {(a,b) : difference between the heights of a and b is less than 5 meters} is the universal-relation.
Solution : It is obvious that the difference between the heights of any two students of the school has to be less than 5 meters. Therefore (a,b) $\in$ R for all a, b $\in$ A.
$\Rightarrow $ R = A X A
$\Rightarrow $ R is the universal-relation on set A.

12th grade math

Home


We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.