Let S be the equivalence relation defined on $P$({1, 2, 3, 4}) defined by XSY if and only if |X| ≡ |Y| (mod 2). Write down the equivalence classes of S.
So the absolute value of any set in $P$({1, 2, 3, 4}) will be any of 0, 1, 2, 3, 4
Aka |X| and |Y| can only equal 0, 1, 2, 3, or 4.
For |X| and |Y| to be congruent (mod 2), |X| - |Y| must be divisible by 2.
So would the equivalence classes just be every 5 different sets, each containing subsets with the same absolute value? As in one set for absolute value 0, one set for absolute value 1, etc. all the way to 4?
I'm confused by what equivalence classes actually are, or what the answer to this would even look like. Thanks for any help.