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: [latex]\mathcal{P}\textrm{(E)}[/latex].

If Card(E) = [latex]n[/latex], then: Card([latex]\mathcal{P}\textrm{(E)}[/latex]) = 2[latex]^{n}[/latex].
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: [latex]\mathcal{P}\textrm{(E)}[/latex] = {∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}.