For set S = {1%2C3%2C5}, show:
Elements, cardinality, and power set
List the elements of S
Elements = set objects
Use the ∈ symbol.
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%2C3%2C5 | {} |
| 1 | 1 | 1%2C3%2C5 | {1%2C3%2C5} |
List our Power Set P in notation form:
P = {{}, {1%2C3%2C5}}
Partition 1
{{1%2C3%2C5})
What is the Answer?
P = {{}, {1%2C3%2C5}}
How does the Power Sets and Set Partitions Calculator work?
Free Power Sets and Set Partitions Calculator - Given a set S, this calculator will determine the power set for S and all the partitions of a set.
This calculator has 1 input.
What 1 formula is used for the Power Sets and Set Partitions Calculator?
The power set P is the set of all subsets of S including S and the empty set ∅.For more math formulas, check out our Formula Dossier
What 7 concepts are covered in the Power Sets and Set Partitions Calculator?
elementan element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.empty setThe set with no elements∅notationAn expression made up of symbols for representing operations, unspecified numbers, relations and any other mathematical objectspartitiona grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.power sets and set partitionsseta collection of different things; a set contains elements or members, which can be mathematical objects of any kindsubsetA is a subset of B if all elements of the set A are elements of the set B
Example calculations for the Power Sets and Set Partitions Calculator
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