If is a relation defined on the set of natural numbers such that if and only if , then is
An equivalence relation
Explanation of the correct Option:
The correct option is D : An equivalence relation
To show the equivalence relation we need to show that the relation is reflexive , symmetric and transitive
Reflexive: Let . Then
(Commutative law of Addition)
is reflexive.
Symmetric: Let such that
. Then
(By commutativity of addition on )
is symmetric.
Transitive : Let such that
and . Then,
∴ and on so is transitive.
Hence is an equivalence relation on .
Therefore ,correct option is (D) An Equivalence Relation