An equivalence relation is a binary relation that fulfills reflexivity, symmetry and transitivity.

A partially ordered set is a set equipped with a binary relation that fulfills reflexivity, antisymmetry and transitivity.

For a partially ordered set, some elements of the set might be incomparable, i.e. $x\le y$ or $y\le x$ may both not hold. That's why we use the term"partially". An example would be $\subset $ as a binary relation and the set M:={{1},{2},{1,2}}. Obviously, {1} and {2} are incomparable.

Question: Can also elements of a set, equipped with an equivalence relation, be incomparable?

A partially ordered set is a set equipped with a binary relation that fulfills reflexivity, antisymmetry and transitivity.

For a partially ordered set, some elements of the set might be incomparable, i.e. $x\le y$ or $y\le x$ may both not hold. That's why we use the term"partially". An example would be $\subset $ as a binary relation and the set M:={{1},{2},{1,2}}. Obviously, {1} and {2} are incomparable.

Question: Can also elements of a set, equipped with an equivalence relation, be incomparable?