Power Sets and Set Partitions Calculator

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

Elements, cardinality, and power set

List the elements of S

Elements = set objects
Use the ∈ symbol.

2 ∈ S
4 ∈ S
6 ∈ S
8 ∈ S
10 ∈ 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 2,4,6,8,10 {}
1 00001 2,4,6,8,10 {10}
2 00010 2,4,6,8,10 {8}
3 00011 2,4,6,8,10 {8,10}
4 00100 2,4,6,8,10 {6}
5 00101 2,4,6,8,10 {6,10}
6 00110 2,4,6,8,10 {6,8}
7 00111 2,4,6,8,10 {6,8,10}
8 01000 2,4,6,8,10 {4}
9 01001 2,4,6,8,10 {4,10}
10 01010 2,4,6,8,10 {4,8}
11 01011 2,4,6,8,10 {4,8,10}
12 01100 2,4,6,8,10 {4,6}
13 01101 2,4,6,8,10 {4,6,10}
14 01110 2,4,6,8,10 {4,6,8}
15 01111 2,4,6,8,10 {4,6,8,10}
16 10000 2,4,6,8,10 {2}
17 10001 2,4,6,8,10 {2,10}
18 10010 2,4,6,8,10 {2,8}
19 10011 2,4,6,8,10 {2,8,10}
20 10100 2,4,6,8,10 {2,6}
21 10101 2,4,6,8,10 {2,6,10}
22 10110 2,4,6,8,10 {2,6,8}
23 10111 2,4,6,8,10 {2,6,8,10}
24 11000 2,4,6,8,10 {2,4}
25 11001 2,4,6,8,10 {2,4,10}
26 11010 2,4,6,8,10 {2,4,8}
27 11011 2,4,6,8,10 {2,4,8,10}
28 11100 2,4,6,8,10 {2,4,6}
29 11101 2,4,6,8,10 {2,4,6,10}
30 11110 2,4,6,8,10 {2,4,6,8}
31 11111 2,4,6,8,10 {2,4,6,8,10}

#	Binary	Use if 1	Subset
0	00000	2,4,6,8,10	{}
1	00001	2,4,6,8,10	{10}
2	00010	2,4,6,8,10	{8}
3	00011	2,4,6,8,10	{8,10}
4	00100	2,4,6,8,10	{6}
5	00101	2,4,6,8,10	{6,10}
6	00110	2,4,6,8,10	{6,8}
7	00111	2,4,6,8,10	{6,8,10}
8	01000	2,4,6,8,10	{4}
9	01001	2,4,6,8,10	{4,10}
10	01010	2,4,6,8,10	{4,8}
11	01011	2,4,6,8,10	{4,8,10}
12	01100	2,4,6,8,10	{4,6}
13	01101	2,4,6,8,10	{4,6,10}
14	01110	2,4,6,8,10	{4,6,8}
15	01111	2,4,6,8,10	{4,6,8,10}
16	10000	2,4,6,8,10	{2}
17	10001	2,4,6,8,10	{2,10}
18	10010	2,4,6,8,10	{2,8}
19	10011	2,4,6,8,10	{2,8,10}
20	10100	2,4,6,8,10	{2,6}
21	10101	2,4,6,8,10	{2,6,10}
22	10110	2,4,6,8,10	{2,6,8}
23	10111	2,4,6,8,10	{2,6,8,10}
24	11000	2,4,6,8,10	{2,4}
25	11001	2,4,6,8,10	{2,4,10}
26	11010	2,4,6,8,10	{2,4,8}
27	11011	2,4,6,8,10	{2,4,8,10}
28	11100	2,4,6,8,10	{2,4,6}
29	11101	2,4,6,8,10	{2,4,6,10}
30	11110	2,4,6,8,10	{2,4,6,8}
31	11111	2,4,6,8,10	{2,4,6,8,10}

List our Power Set P in notation form:

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}}

Partition 1

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

Partition 2

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

Partition 3

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

Partition 4

{6,10},

Partition 5

{6,10},

Partition 6

{6,10},

Partition 7

{6,8},

Partition 8

{6,8},

Partition 9

{6,8},

Partition 10

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

Partition 11

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

Partition 12

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

Partition 13

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

Partition 14

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

Partition 15

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

Partition 16

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

Partition 17

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

Partition 18

{4,8,10},

Partition 19

{4,8,10},

Partition 20

{4,6},

Partition 21

{4,6},

Partition 22

{4,6},

Partition 23

{4,6,10},

Partition 24

{4,6,10},

Partition 25

{4,6,8},

Partition 26

{4,6,8},

Partition 27

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

Partition 28

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

Partition 29

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

Partition 30

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

Partition 31

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

Partition 32

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

Partition 33

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

Partition 34

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

Partition 35

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

Partition 36

{2,6},

Partition 37

{2,6},

Partition 38

{2,6},

Partition 39

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

Partition 40

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

Partition 41

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

Partition 42

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

Partition 43

{2,6,8,10},

Partition 44

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

Partition 45

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

Partition 46

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

Partition 47

{2,4,10},

Partition 48

{2,4,10},

Partition 49

{2,4,8},

Partition 50

{2,4,8},

Partition 51

{2,4,8,10},

Partition 52

{2,4,6},

Partition 53

{2,4,6},

Partition 54

{2,4,6,10},

Partition 55

{2,4,6,8},

Partition 56

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

Power Sets and Set Partitions Calculator

Enter Set

List the elements of S

Cardinality of set S → |S|:

Determine the power set P:

Calculate power set subsets

Build subsets of P

List our Power Set P in notation form:

Partition 1

Partition 2

Partition 3

Partition 4

Partition 5

Partition 6

Partition 7

Partition 8

Partition 9

Partition 10

Partition 11

Partition 12

Partition 13

Partition 14

Partition 15

Partition 16

Partition 17

Partition 18

Partition 19

Partition 20

Partition 21

Partition 22

Partition 23

Partition 24

Partition 25

Partition 26

Partition 27

Partition 28

Partition 29

Partition 30

Partition 31

Partition 32

Partition 33

Partition 34

Partition 35

Partition 36

Partition 37

Partition 38

Partition 39

Partition 40

Partition 41

Partition 42

Partition 43

Partition 44

Partition 45

Partition 46

Partition 47

Partition 48

Partition 49

Partition 50

Partition 51

Partition 52

Partition 53

Partition 54

Partition 55

Partition 56

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