Set \(\mathcal{P}\) of disjoint

subsets of a set E with these two properties:

- Each subset of \(\mathcal{P}\) is not empty;
- The union of all the subsets of E in \(\mathcal{P}\) is equal to E.

- A partition of a set is a kind of classification of the elements in a set by an equivalence relationship.
- The concepts of partitions, equivalence relations, and quotient sets are closely linked. In fact, any equivalence relation \(\mathcal{R}\) defined in a set E causes in this set a partition \(\wp\) into classes of equivalences. The set \(\wp\) of these classes is called the
**quotient set** of E by the equivalence relation ℜ and is noted as: E / ℜ.

### Example

Consider the partition \(\wp\) of a set E:

- E = {
*a, b, c, d, e, f, g h, i*}
- \(\wp\) = {{
*a, b, c, d*}, {*e, f*}, {*g*}, {*h*, *i*}}