Let's check for reflexive first
aRa = a-a = 0 which is not odd positive integer. So option b), c), d) gets eliminated because reflexive is necessary for these three options. d) is the answer clearly but let's see how?
A relation is antisymmetric if aRb is in relation and if bRa is also in relation then a=b that means diagonal elements like (1,1), (2,2) etc can be present, it is not compulsory that they should be present. However elements like (3,2) , (5,2) if present then (2,3) , (2,5) must not be present because a=b property voilates.
So for the given relation If we try to find out the elements then it should be like..
R = { (2,1) , (5,2) , (6,1) ........etc}
Clearly R is antisymmetric.
Option a) is correct answer