The given relation R is equivalence relation(since it satisfies reflexive,symmetric,transitive properties).
The given equivalence relation R partitions the domain into 3 non empty,disjoint,exhaustive subsets {1,4,7,10}, {2,5,8}, {3,6,9}.
Together these 3 subsets form a partition.
we have to form the ordered pairs in equivalence relation from the partition.
The ordered pairs from {1,3,7,10}={(1,1),(1,4),(1,7),(1,10),(4,1),(4,4),(4,7),(4,10),(7,1)(7,4),(7,7),(7,10),(10,1),(10,4),(10,7),(10,10)}
or for the ordered pair(x,y) from the subset {1,3,7,10}, x has 4 choices and y also has 4 choices.
Therefore 16 ordered pairs are formed from subset {1,3,7,10}.
The ordered pairs from {2,5,8}={(2,2),(2,5),(2,8),(5,2),(5,5),(5,8),(8,2),(8,5),(8,8).
or for the ordered pair (x,y) from the subset {2,5,8} ,x has 3 choices and y also has 3 choices.
Therefore 9 ordered pairs are formed from subset {2,5,8}.
similarly 9 order pairs are formed from subset {3,6,9}.
Therefore there are 16+9+9=34 ordered pairs possible.