Name given to each subset of a set E.

### Symbol

A set whose elements include all of the subsets or parts of a set E is noted like this: \(\mathcal{P}\textrm{(E)}\).

- If Card(E) = \(n\), then: Card(\(\mathcal{P}\textrm{(E)}\)) = 2\(^{n}\).
- A part of a set E that is different from E and not empty is called a proper part of a set E.

### Example

Consider: E = {1, 2, 3}.

Therefore: \(\mathcal{P}\textrm{(E)}\) = {∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}.