Relations & Type of Relation

Relation means in the real world how closely they know each other

there are many types of relation

Perfect positive relation -very Close

Positive relation -Close to each-other

Negative relation -Apart from each-other

Perfect negative relation -Very apart

If (a,b)∈R,We can say that a is related to b under the relation R

and mathematically it can be written as aRb

Types of Relation

Empty relation

A relation R in set A is called empty relation if no element of A is related to any element of A

i.e. R=Φ⊂AxA

Universal Relation

A relation R in set A is called \universal relation if each element of A is related to every element of A

R=AXA

Both the empty and universal relation are called trivial relation.

A relation R in set A is called.

1) Reflexive if (a,a)∈R,for every a∈R

2)Symmetric if (a,b)∈R implies that (b,a)∈R for all a,b∈A

3)Transitive if (a,b)∈R and (b,c)∈R implies that (a,c)∈R for all a,b,c∈A

A relation R in set A is called an equivalence relation if R is Reflexive, Symmetric and Transitive.