The relation ‘less than’ in the set of natural numbers is
only transitive
Explanation for correct option
Option (B): only transitive
In a transitive relation, if and then
Here, relation is ‘less than’, so and then
For example: Let and
Here, and , so , which is true.
Thus option(B) is correct.
Explanation for incorrect options
Option (A): only symmetric
In a symmetric relation, if then
Here, relation is ‘less than’, so then
For example: Let and
Here, but is not true.
Thus option(A) is incorrect.
Option (C): only reflexive
In a reflexive relation,
Here, relation is ‘less than’, so
For example: Let so which is not true.
Thus option(C) is incorrect.
Option (D): equivalence relation
A relation on a set is said to be equivalent if and only if the relation is reflexive, symmetric and transitive.
As the given relation is not symmetric and reflexive, so it is not an equivalence relation.
Thus option(D) is incorrect.
Hence, the correct option is option(B) i.e. only transitive