The intervals of real numbers (−∞;0[ , [0;+∞) constitute equivalence classes on ℝ. True or false?

Question

There is no further information given. My thoughts on this question are if there can be equivalence classes if there is no equivalence relation?

Thank you in advance !

Answer 1

True. You are given a partition of $R$. There is a fundamental relationship between partitions and equivalence relations. The equivalence relation here is that $a$ is related to $b$ if and only if they are in the same set.