>>14210957Someone please help a dying math major
I'm given the following equivalence relation on S5, with S3 being any permutation of {1,2,3}:
The question: Determine the total number of equivalence classes.
Is there a way to do this that isn't aggregiously tedious? I've already found (4,5) to have 6 distinct permutations in its equivalence class, and (1,2,3,4,5) to also have 6. I know there are 24 distinct permutations in S5, so my intuition tells me there are two more equivalence classes of 6 elements, totalling 4 equivalence classes in S5 under this relation. I have no idea how to go about verifying this. Please help
