Solution Found!
Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a
Chapter 9, Problem 9.19(choose chapter or problem)
Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a completeset of equivalence class representatives in each of the following special cases.(a) S = {I, 2, ... , n} and G = S".(b) S = {I, 2, 3, 4) and G = (Ci), (2 3)}.(c) S={I, 2, 3, 4, 5}andG={(I),(1 2),(1 3),(23),(123),(13 2)}.
Questions & Answers
QUESTION:
Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a completeset of equivalence class representatives in each of the following special cases.(a) S = {I, 2, ... , n} and G = S".(b) S = {I, 2, 3, 4) and G = (Ci), (2 3)}.(c) S={I, 2, 3, 4, 5}andG={(I),(1 2),(1 3),(23),(123),(13 2)}.
ANSWER:Step 1 of 4
Consider the relation on permutation group G on S and define on S by
If for some.
Then is an equivalence relation on S.
Now, we need to find different equivalence classes in the following cases.