Tuesday, February 12, 2019

Types of Relation


What are the Types of Relations?


1. Empty Relation
2. Universal Relation
3. Reflexive Relation
4. Symmetric Relation
5. Transitive Relation




1   1.     What is Empty Relation?

                       A Relation R in any set say A is said to be Empty Relation if no elements of                               Set A is related no elements of itself.
                              i.e.  R = ะค  A×A.

2.      What is Universal Relation? 

                                  A Relation R in any set say A is said to be Universal Relation if all elements of Set A is related to its all elements.
                            i.e.  R = A×A.

     3.  What is Reflexive Relation? 

                             A Relation R in any set say A is said to be Reflexive Relation if all same elements present in any Relation.
     i.e. if (a, a) R, for every a A.
     For Example R = {(1, 1), (2, 2), (a, a), (x, x)}
    

         4.   What is Symmetric Relation?

                            A Relation R in any set say A is said to be Symmetric Relation if all same elements present in any Relation R then its mirror image also presents in that Relation.
      i.e. if (a, b) R,  then it implies (b, a)  R for all a, b A.
      For Example R = {(1, 2), (2, 1), (a, b), (b, a), (x, y), (y, x)}
    

     5. What is Transitive Relation?  

                              A Relation R in any set say A is said to be Transitive Relation 
       i.e. if (a, b) R,  (b, c)  R then it implies (a, c)  R for all a, b, c A.
       For Example R = {(1, 2), (2, 1), (1, 1), (b, a), (a, y), (b, y)}
      

        Note:    Equivalence Relation:

                        A Relation R which is Reflexive, Symmetric and Transitive said to be equivalence Relation.



                                  

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