Prove that the equivalence classes of an equivalence relation are disjoint.
140724
How to prove two equivalence classes are disjoint?
17363
Prove that the intersection of two equivalence relations is an equivalence relation.
55661
Existence of two disjoint closed sets with zero infimal distance
123090
How to show that disjoint closed sets have disjoint open supersets?
11342
Show that conguence $\bmod m\,$ is an equivalence relation
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
150064
Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
91777
Product of Non-Disjoint Cycles
36566
Equivalence classes and metric spaces
24685
Expressing a Countable Union of Sets as the Countable Union of Disjoint Sets (e.g. Eliminating Duplicate Intersections)
104977
How to calculate equivalence relations
62936
Proving equivalencies of two versions of the Axiom of Choice
96025
Showing there is only one isomorphism between well ordered sets using transfinite induction
80209
If $X,Y$ are equivalence relations, so is $X \times Y$
145273
Disjoint $AC$ equivalent to $AC$
60231
Number of equivalence classes of matrices under switching rows and columns