The relation R on A={0,1,2,…,9} is defined by (x,y)∈R iff ∣x−y∣ is a multiple of 3, i.e., x≡y(mod3).
Statement II:
R is reflexive (∣x−x∣=0, a multiple of 3), symmetric (∣x−y∣=∣y−x∣), and transitive (if x≡y and y≡z(mod3), then x≡z(mod3)). So R is an equivalence relation. Statement II is correct.
Statement I:
The equivalence classes are {0,3,6,9} (4 elements), {1,4,7} (3 elements), {2,5,8} (3 elements).
n(R)=42+32+32=16+9+9=34=36. Statement I is incorrect.