Let $A = \{0,1,2,3,4\}$ and define a relation $R$ on $A$ as follows:
$$R = \{(0,0),(0,4),(1,1),(1,3),(2,2),(3,1),(3,3),(4,0),(4,4)\}.$$
Find the distinct equivalence classes of $R$.
How do I solve this problem? What is an equivalence class? As I understand it so far, the equivalence class of $a$, is the set of all elements $x$ in $A$ such that $x$ is related to $a$ by $R$. What does this mean in my problems case?
Best Answer
The equivalence classes are $\{0,4\},\{1,3\},\{2\}$. to see this you should first check your relation is indeed an equivalence relation. After this find all the elements related to $0$. Then pick the next smallest number not related to zero and find all the elements related to it and so on until you have processed each number.