is a relation that is
reflexive and transitive
Reflexive relation: A relation is reflexive on a set , if ,
Symmetric relation: A relation is symmetric on a set , if then ,
Transitive relation: A relation is reflexive on a set , if and then ,
Explanation for the correct option:
reflexive and transitive
Let be the relation
Reflexive:
Hence, the relation is reflexive.
Symmetric:
If , then
If , then
Hence, the relation is not symmetric.
Transitive:
If , then ….(1)
If , then ….(2)
Multiply equations (1) and (2)
Since so .
Hence, the relation is transitive.
Therefore, the correct option is reflexive and transitive.