... 1061.3. RELATIONS AND PARTITIONS 19Definition 1.3.9 (Partition of a set). Let A be a non-empty set. Then a partition Π of A, intom-parts, is a collection of non-empty subsets A1, A2, . ... non-empty set with an equivalence relation ∼. Then the equivalenceclasses of ∼ in A, gives rise to a partition of A. Conversely, given any partition Π of A, there isan equivalence relation on ... y) : x ∈ R}.Definition 1.3.3 (Relation). A relation R on a non-empty set A, is a subset of A × A.Example 1.3.4. 1. Le t A = {a, b, c, d}. Then, some of the re lations R on A are:(a) R = A ×A.(b)...