For set S = {b,c,f}, show:
Elements, cardinality, and power set
List the elements of S
Elements = set objects
Use the ∈ symbol.
- b ∈ S
- c ∈ S
- f ∈ S
Cardinality of set S → |S|:
Cardinality = Number of set elements.
Since the set S contains 3 elements
|S| = 3
Determine the power set P:
Power set = Set of all subsets of S
including S and ∅.
Calculate power set subsets
S contains 3 terms
Power Set contains 23 = 8 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 | 000 | {} | |
| 1 | 001 | {f} | |
| 2 | 010 | {c} | |
| 3 | 011 | {c,f} | |
| 4 | 100 | b, | {b} |
| 5 | 101 | b, | {b,f} |
| 6 | 110 | b,c, | {b,c} |
| 7 | 111 | b,c,f | {b,c,f} |
List our Power Set P in notation form:
P = {{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}
Partition 1
{c,f},{b}
Partition 2
{b,f},
Partition 3
{b,c},
Partition 4
{{b},{c},{f})
What is the Answer?
P = {{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}
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.
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 ∅.
What 7 concepts are covered in the Power Sets and Set Partitions Calculator?
- element
- an 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 set
- The set with no elements
∅ - notation
- An expression made up of symbols for representing operations, unspecified numbers, relations and any other mathematical objects
- partition
- a 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 partitions
- set
- a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
- subset
- A is a subset of B if all elements of the set A are elements of the set B
