Equivalence relation Mathematical base In Computer science
In order to prove that $U$ is an equivalence relation, you need to use the definition: prove that $U$ is reflexive, symmetric and transitive. If you try to do that but it doesn't work, you can try to disprove the claim that $U$ is always an equivalence relation by giving a counterexample: equivalence relations $R$ and $S$ such that the corresponding $U$ isn't an equivalence relation (that is, it either isn't reflexive, isn't symmetric or isn't transitive); you can use your failed proof attempts to guide you in the construction.