Question

#What is trivial relations? <br />#what is arbitrary equivalence relations?<br /><br /><br /><br />Explain above in simple language. <br /><br /><br /><br />If not know pls don't earn points. <br /><br /><br />I am not able to understand pls explain. <br /><br /><br /> THANK YOU ​

Answer 1

Hi it can help you.

Answer 2

The relation which equals the product of the sets on which it is defined is called trivial relation.

1) A relation R in a set A is called empty relation, if no element of A is

related to any element of A, i.e., R = φ ⊂ A × A.

2) A relation R in a set A is called universal relation, if each element of A

is related to every element of A, i.e., R = A × A.

So both relations are trivial relation.

As they are equal to product of A on which they are defined.

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation, where for any objects a, b, and c:

a = a (reflexive property),

if a = b then b = a (symmetric property), and

if a = b and b = c then a = c (transitive property).

As a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.

****HOPE YOU UNDERSTAND ****

THANK YOU