Question

Let A = {1,2,3,4} and let R = {(1,1), (1,2),(2,1),(2,2),(3,4),(4,3), (3,3), (4,4)} be an equivalence relation on R. Determine A/R.

Answer 1

Let $A = \{1,2,3,4\}$ and let $R = \{(1,1), (1,2),(2,1),(2,2),(3,4),(4,3), (3,3), (4,4)\}$ be an equivalence relation on $R$. Let us determine $A/R$ . Taking into account that $[a]=\{x\in A\ |\ (x,a)\in R\}$ and hence $[1]=\{1,2\}=[2],\ [3]=\{3,4\}=[4],$ we conclude that $A/R=\{[a]\ |\ a\in A\}=\{[1],[3]\}$ .