I am currently taking discrete math and have been given the following question to answer.
Given $S=\{0,1,2,3,4,5\}$, find the partition induced by the equivalence relation $R$ where $R=\{(0,0),(0,4),(1,1),(1,3),(4,5),(0,5),(5,4),(5,0),(5,5),(2,2),(3,1),(3,3),(4,0),(4,4)\}$. Explain.
For this I got $\{0,4,5\}, \{1,3\}, \{2\}$ \begin{align*} [0],[4],[5] &= \{0,4,5\}\\ [2] &= \{2\}\\ [1],[3] &= \{1,3\}\\ \end{align*}
Does this look correct?