The idea of congruency is not new so that was pretty straight forward. I'm not sure that I could recreate the proof for the symmetric case from memory though. Remembering how to do the proofs for the different properties of equivalence relations is still a little difficult.
I liked the significance of the equivalence sets when related to the congruent to modulo relation. The way to interpret the equivalence sets and determine how many distinct sets should exist, is an interesting idea as well.
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