Final answer:
The relation {(0,0), (1,1), (2,2), (3,3)} forms an equivalence relation with the equivalence classes {0}, {1}, {2}, and {3}.
Step-by-step explanation:
The relation {(0,0), (1,1), (2,2), (3,3)} defines an equivalence relation. In order to find the equivalence classes, we need to determine the groups of elements that are related to each other through this relation.
Considering {(0,0)}, the equivalence class is {0}. Similarly, the equivalence classes for {(1,1)}, {(2,2)}, and {(3,3)} are {1}, {2}, and {3} respectively.
Therefore, the equivalence classes for the given relation are {0}, {1}, {2}, and {3}.