For set S = {1,2,3,4,5}, show:
Elements, cardinality, and power set
List the elements of S
Elements = set objects
Use the ∈ symbol.
- 1 ∈ S
- 2 ∈ S
- 3 ∈ S
- 4 ∈ S
- 5 ∈ S
Cardinality of set S → |S|:
Cardinality = Number of set elements.
Since the set S contains 5 elements
|S| = 5
Determine the power set P:
Power set = Set of all subsets of S
including S and ∅.
Calculate power set subsets
S contains 5 terms
Power Set contains 25 = 32 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 | 00000 | {} | |
| 1 | 00001 | {5} | |
| 2 | 00010 | {4} | |
| 3 | 00011 | {4,5} | |
| 4 | 00100 | {3} | |
| 5 | 00101 | {3,5} | |
| 6 | 00110 | {3,4} | |
| 7 | 00111 | {3,4,5} | |
| 8 | 01000 | {2} | |
| 9 | 01001 | {2,5} | |
| 10 | 01010 | {2,4} | |
| 11 | 01011 | {2,4,5} | |
| 12 | 01100 | {2,3} | |
| 13 | 01101 | {2,3,5} | |
| 14 | 01110 | {2,3,4} | |
| 15 | 01111 | {2,3,4,5} | |
| 16 | 10000 | 1, | {1} |
| 17 | 10001 | 1, | {1,5} |
| 18 | 10010 | 1, | {1,4} |
| 19 | 10011 | 1, | {1,4,5} |
| 20 | 10100 | 1, | {1,3} |
| 21 | 10101 | 1, | {1,3,5} |
| 22 | 10110 | 1, | {1,3,4} |
| 23 | 10111 | 1, | {1,3,4,5} |
| 24 | 11000 | 1,2, | {1,2} |
| 25 | 11001 | 1,2, | {1,2,5} |
| 26 | 11010 | 1,2, | {1,2,4} |
| 27 | 11011 | 1,2, | {1,2,4,5} |
| 28 | 11100 | 1,2,3, | {1,2,3} |
| 29 | 11101 | 1,2,3, | {1,2,3,5} |
| 30 | 11110 | 1,2,3,4, | {1,2,3,4} |
| 31 | 11111 | 1,2,3,4,5 | {1,2,3,4,5} |
List our Power Set P in notation form:
You have 2 free calculationss remaining
Partition 1
{4,5},{1,2,3}
Partition 2
{4,5},{1,2,3}
Partition 3
{4,5},{1,2,3}
Partition 4
{3,5},
Partition 5
{3,5},
Partition 6
{3,5},
Partition 7
{3,4},
Partition 8
{3,4},
Partition 9
{3,4},
Partition 10
{3,4,5},{1,2}
Partition 11
{3,4,5},{1,2}
Partition 12
{2,5},{1,2,3}
Partition 13
{2,5},{1,2,3}
Partition 14
{2,5},{1,2,3}
Partition 15
{2,4},{1,2,3}
Partition 16
{2,4},{1,2,3}
Partition 17
{2,4},{1,2,3}
Partition 18
{2,4,5},
Partition 19
{2,4,5},
Partition 20
{2,3},
Partition 21
{2,3},
Partition 22
{2,3},
Partition 23
{2,3,5},
Partition 24
{2,3,5},
Partition 25
{2,3,4},
Partition 26
{2,3,4},
Partition 27
{2,3,4,5},{1}
Partition 28
{1,5},{1,2,3}
Partition 29
{1,5},{1,2,3}
Partition 30
{1,5},{1,2,3}
Partition 31
{1,4},{1,2,3}
Partition 32
{1,4},{1,2,3}
Partition 33
{1,4},{1,2,3}
Partition 34
{1,4,5},{1,2}
Partition 35
{1,4,5},{1,2}
Partition 36
{1,3},
Partition 37
{1,3},
Partition 38
{1,3},
Partition 39
{1,3,5},{1,2}
Partition 40
{1,3,5},{1,2}
Partition 41
{1,3,4},{1,2}
Partition 42
{1,3,4},{1,2}
Partition 43
{1,3,4,5},
Partition 44
{1,2},{1,2,3}
Partition 45
{1,2},{1,2,3}
Partition 46
{1,2},{1,2,3}
Partition 47
{1,2,5},
Partition 48
{1,2,5},
Partition 49
{1,2,4},
Partition 50
{1,2,4},
Partition 51
{1,2,4,5},
Partition 52
{1,2,3},
Partition 53
{1,2,3},
Partition 54
{1,2,3,5},
Partition 55
{1,2,3,4},
Partition 56
{{1},{2},{3},{4},{5})
What is the Answer?
How does the Power Sets and Set Partitions Calculator work?
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What 1 formula is used for the Power Sets and Set Partitions Calculator?
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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
Example calculations for the Power Sets and Set Partitions Calculator
Power Sets and Set Partitions Calculator Video
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