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?

Answer 1

might as well be a triangle ...

Answer 2

1 3 2
2 3 rotate to the left 1 2 rotate again 3 1


to account for the flips ... start at teh begining again

1 1
2 3 flip over 1 3 2


1 3
2 3 flip over 2 2 1


1 2
2 3 flip over 3 1 3

Answer 3

we can define 3 instances of rotate: r^0, r^1, r^2

we can define 1 instance of flip: f^1

we can use these to get to any of the 6 outcomes ... and somehow show equivalences with them

Answer 4

with reviewing some material ... thats about as far as i can remember :/