For set S = {1}, show:
Elements, cardinality, and power set
List the elements of S
Elements = set objects
Use the ∈ symbol.
- 1 ∈ S
Cardinality of set S → |S|:
Cardinality = Number of set elements.
Since the set S contains 1 elements
|S| = 1
Determine the power set P:
Power set = Set of all subsets of S
including S and ∅.
Calculate power set subsets
S contains 1 terms
Power Set contains 21 = 2 items
Build subsets of P
The subset A of a set B is
A set where all elements of A are in B.
| # | Binary | Use if 1 | Subset |
|---|---|---|---|
| 0 | 0 | {} | |
| 1 | 1 | 1 | {1} |
List our Power Set P in notation form:
P = {{}, {1}}
Partition 1
{{1})
