# Part of a Set E

## Part of a Set E

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}}.