n Example 8.11, we considered the relation M := {(m, d i ): in some years, month m has d days}, and computed the pairs in the relation M −1 ◦ M. By checking all the requirements (or by visual...

n Example 8.11, we considered the relation M := {(m, d_i
): in some years, month m has d days}, and computed the pairs in the relation M⁻¹
◦ M. By checking all the requirements (or by visual inspection of Figure 8.13(b)), we see that M⁻¹
◦ M is an equivalence relation. But it turns out that the fact that M−1 ◦ M is an equivalence relation says something particular about M, and is not true in general. Let R ⊆ A × B be an arbitrary relation. Prove or disprove whether R−1 ◦ R must have the three required properties of an equivalence relation (at least one of these is false!