Discrete Math: Relations: A round bracelet has three beads equidistant from each other. The top bead is red, the left lower bead is blue, and the right lower bead is white. Define a relation R between bracelets as: (B1,B2), where B1and 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?

Question

Discrete Math: Relations: A round bracelet has three beads equidistant from each other. The top bead is red, the left lower bead is blue, and the right lower bead is white. Define a relation R between bracelets as: (B1,B2), where B1and 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?