Consider the relation R on S 1234 R 11223344 Which best de

Consider the relation R on S = {1.2.3.4}: R = {(1.1).(2,2).(3.3).{4.4)}. Which best describe R? It is Reflexive but Dot Symmetric. It is Symmetric but not Reflexive. It b an Equivalence Relation. It is a Partial Ordering. It is an Equivalence Relation and a Partial Ordering...

Solution

The relation S = {1,2,3,4} given by R= {(1,1), (2,2) , (3,3), (4,4) } is reflexive because all loops are present. The given relation is not symmetric because all paths are not 2-way. And clearly is not transitive. Since the relation only satisfies the reflexive property hence it is not an equivalence relation.

Therefore (a) is the correct option.