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]\\}" .
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