Date: Oct 6, 2012 5:38 PM
Author: Edward
Subject: Sets Forming Partitions
So I have been learning about binary and equivalence relations and things have been going smoothly. I have a question about partitions though because I'm not sure how to finish this problem:

2. Which of the following collections of subsets of S={1,2,3,4,5,6} form a partition of S? If the given collection of sets does form a partition, then list the ordered pairs if the equivalence relation produced by the partition. If the given collection does not form a partition, then explain which part(s) of the definition of partition fails.

(a.) {1,3}, {5,4}, {2,6}

This is a partition of S.

(b.) {1,2,3}, {3,4}, {5,6}

This is not a partition of S.

(c.) {1}, {2}, {5}, {4,3,6}

This is a partition of S.

(d.) {1,3,4}, {2,6}

This is a partition of S.

Under each letter I figured out if the sets form a partition of S but I don't understand how to then list the ordered pairs if the equivalence relation produced by the partition if it is or explain which part(s) of the definition of partition fails. I'm halfway there I just need to understand how I to prove my answer..... If somebody could help me understand this I would really appreciate it