For set S = {2,4,6,8,10}, show:

Elements, cardinality, and power set

Elements = set objects

Use the ∈ symbol.

- 2 ∈ S
- 4 ∈ S
- 6 ∈ S
- 8 ∈ S
- 10 ∈ S

Cardinality = Number of set elements.

Since the set S contains 5 elements

|S| = **5**

Power set = Set of all subsets of S

including S and ∅.

S contains 5 terms

Power Set contains 2^{5} = 32 items

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 | {10} | |

2 | 00010 | {8} | |

3 | 00011 | {8,10} | |

4 | 00100 | {6} | |

5 | 00101 | {6,10} | |

6 | 00110 | {6,8} | |

7 | 00111 | {6,8,10} | |

8 | 01000 | {4} | |

9 | 01001 | {4,10} | |

10 | 01010 | {4,8} | |

11 | 01011 | {4,8,10} | |

12 | 01100 | {4,6} | |

13 | 01101 | {4,6,10} | |

14 | 01110 | {4,6,8} | |

15 | 01111 | {4,6,8,10} | |

16 | 10000 | 2, | {2} |

17 | 10001 | 2, | {2,10} |

18 | 10010 | 2, | {2,8} |

19 | 10011 | 2, | {2,8,10} |

20 | 10100 | 2, | {2,6} |

21 | 10101 | 2, | {2,6,10} |

22 | 10110 | 2, | {2,6,8} |

23 | 10111 | 2, | {2,6,8,10} |

24 | 11000 | 2,4, | {2,4} |

25 | 11001 | 2,4, | {2,4,10} |

26 | 11010 | 2,4, | {2,4,8} |

27 | 11011 | 2,4, | {2,4,8,10} |

28 | 11100 | 2,4,6, | {2,4,6} |

29 | 11101 | 2,4,6, | {2,4,6,10} |

30 | 11110 | 2,4,6,8, | {2,4,6,8} |

31 | 11111 | 2,4,6,8,10 | {2,4,6,8,10} |

P = **{{}, {2}, {4}, {6}, {8}, {10}, {2,10}, {2,4}, {2,6}, {2,8}, {4,10}, {4,6}, {4,8}, {6,10}, {6,8}, {8,10}, {2,4,10}, {2,4,6}, {2,4,8}, {2,6,10}, {2,6,8}, {2,8,10}, {4,6,10}, {4,6,8}, {4,8,10}, {6,8,10}, {2,4,6,10}, {2,4,6,8}, {2,4,8,10}, {2,6,8,10}, {4,6,8,10}, {2,4,6,8,10}}**

{8,10},{2,4,6}

{8,10},{2,4,6}

{8,10},{2,4,6}

{6,10},

{6,10},

{6,10},

{6,8},

{6,8},

{6,8},

{6,8,10},{2,4}

{6,8,10},{2,4}

{4,10},{2,4,6}

{4,10},{2,4,6}

{4,10},{2,4,6}

{4,8},{2,4,6}

{4,8},{2,4,6}

{4,8},{2,4,6}

{4,8,10},

{4,8,10},

{4,6},

{4,6},

{4,6},

{4,6,10},

{4,6,10},

{4,6,8},

{4,6,8},

{4,6,8,10},{2}

{2,10},{2,4,6}

{2,10},{2,4,6}

{2,10},{2,4,6}

{2,8},{2,4,6}

{2,8},{2,4,6}

{2,8},{2,4,6}

{2,8,10},{2,4}

{2,8,10},{2,4}

{2,6},

{2,6},

{2,6},

{2,6,10},{2,4}

{2,6,10},{2,4}

{2,6,8},{2,4}

{2,6,8},{2,4}

{2,6,8,10},

{2,4},{2,4,6}

{2,4},{2,4,6}

{2,4},{2,4,6}

{2,4,10},

{2,4,10},

{2,4,8},

{2,4,8},

{2,4,8,10},

{2,4,6},

{2,4,6},

{2,4,6,10},

{2,4,6,8},

{{2},{4},{6},{8},{10})

P = **{{}, {2}, {4}, {6}, {8}, {10}, {2,10}, {2,4}, {2,6}, {2,8}, {4,10}, {4,6}, {4,8}, {6,10}, {6,8}, {8,10}, {2,4,10}, {2,4,6}, {2,4,8}, {2,6,10}, {2,6,8}, {2,8,10}, {4,6,10}, {4,6,8}, {4,8,10}, {6,8,10}, {2,4,6,10}, {2,4,6,8}, {2,4,8,10}, {2,6,8,10}, {4,6,8,10}, {2,4,6,8,10}}**

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.

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

For more math formulas, check out our Formula Dossier

- 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

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