Answer:
The given relation R is equivalence relation.
Step-by-step explanation:
Given that:

Where
is the relation on the set of ordered pairs of positive integers.
To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.
1. First of all, let us check reflexive property:
Reflexive property means:

Here we need to prove:

As per the given relation:
which is true.
R is reflexive.
2. Now, let us check symmetric property:
Symmetric property means:

Here we need to prove:

As per the given relation:
means 
means 
Hence true.
R is symmetric.
3. R to be transitive, we need to prove:

means
.... (1)
means
...... (2)
To prove:
To be
we need to prove: 
Multiply (1) with (2):

So, R is transitive as well.
Hence proved that R is an equivalence relation.