Solved: Each bead on a bracelet with three beads is either

Chapter 8, Problem 8.5.58

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Each bead on a bracelet with three beads is either red, white, or blue, as illustrated in the figure shown. Bead I Red Bead 30 Bead 2 Blue White Define the relation R between bracelets as: (BI , B2), where B I and B2 are bracelets, belongs to R if and only if B2 can be obtained from B1 by rotating it or rotating it and then reflecting it. a) Show that R is an equivalence relation. b) What are the equivalence classes of R?

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