UPSC NDA Math Model Paper 2

Let's check the given relation for its type one by one.
Reflexive: xRx = x - x + π = π, which is irrational. Therefore, R is reflexive.
Symmetric: Let's say that xRy is true i.e. x - y + π is irrational. Now, yRx = y - x + π will also be irrational. It means, if xRy, then yRx. Therefore, Ris symmetric.
Transitive: If xRy and yRz are true, then xRz = x - z + π = (x - y + π) + (y - z + π) - 2π + π is irrational. Therefore, R is transitive.
Since the relation R is reflexive, symmetric and transitive as well, it is an equivalence relation.