- Let ~ be the relation on $\mathbb R$ defined by
a ~ b if and only if |a| = |b|:
(a) Prove that is an equivalence relation.
(b) Give an example of an equivalence class with two elements.
(c) Give an example of an equivalence class with one element.
(d) Give a complete set of equivalence class representatives.
I can do part (a) of the question by showing the symmetry, reflexivity and transitivity but I'm struggling with the rest of the question. Can anyone give me some hints?