For set S = {a,i,l,r,s,t,u}, show:
Elements, cardinality, and power set
List the elements of S
Elements = set objects
Use the ∈ symbol.
- a ∈ S
- i ∈ S
- l ∈ S
- r ∈ S
- s ∈ S
- t ∈ S
- u ∈ S
Cardinality of set S → |S|:
Cardinality = Number of set elements.
Since the set S contains 7 elements
|S| = 7
Determine the power set P:
Power set = Set of all subsets of S
including S and ∅.
Calculate power set subsets
S contains 7 terms
Power Set contains 27 = 128 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 | 0000000 | {} | |
| 1 | 0000001 | {u} | |
| 2 | 0000010 | {t} | |
| 3 | 0000011 | {t,u} | |
| 4 | 0000100 | {s} | |
| 5 | 0000101 | {s,u} | |
| 6 | 0000110 | {s,t} | |
| 7 | 0000111 | {s,t,u} | |
| 8 | 0001000 | {r} | |
| 9 | 0001001 | {r,u} | |
| 10 | 0001010 | {r,t} | |
| 11 | 0001011 | {r,t,u} | |
| 12 | 0001100 | {r,s} | |
| 13 | 0001101 | {r,s,u} | |
| 14 | 0001110 | {r,s,t} | |
| 15 | 0001111 | {r,s,t,u} | |
| 16 | 0010000 | {l} | |
| 17 | 0010001 | {l,u} | |
| 18 | 0010010 | {l,t} | |
| 19 | 0010011 | {l,t,u} | |
| 20 | 0010100 | {l,s} | |
| 21 | 0010101 | {l,s,u} | |
| 22 | 0010110 | {l,s,t} | |
| 23 | 0010111 | {l,s,t,u} | |
| 24 | 0011000 | {l,r} | |
| 25 | 0011001 | {l,r,u} | |
| 26 | 0011010 | {l,r,t} | |
| 27 | 0011011 | {l,r,t,u} | |
| 28 | 0011100 | {l,r,s} | |
| 29 | 0011101 | {l,r,s,u} | |
| 30 | 0011110 | {l,r,s,t} | |
| 31 | 0011111 | {l,r,s,t,u} | |
| 32 | 0100000 | {i} | |
| 33 | 0100001 | {i,u} | |
| 34 | 0100010 | {i,t} | |
| 35 | 0100011 | {i,t,u} | |
| 36 | 0100100 | {i,s} | |
| 37 | 0100101 | {i,s,u} | |
| 38 | 0100110 | {i,s,t} | |
| 39 | 0100111 | {i,s,t,u} | |
| 40 | 0101000 | {i,r} | |
| 41 | 0101001 | {i,r,u} | |
| 42 | 0101010 | {i,r,t} | |
| 43 | 0101011 | {i,r,t,u} | |
| 44 | 0101100 | {i,r,s} | |
| 45 | 0101101 | {i,r,s,u} | |
| 46 | 0101110 | {i,r,s,t} | |
| 47 | 0101111 | {i,r,s,t,u} | |
| 48 | 0110000 | {i,l} | |
| 49 | 0110001 | {i,l,u} | |
| 50 | 0110010 | {i,l,t} | |
| 51 | 0110011 | {i,l,t,u} | |
| 52 | 0110100 | {i,l,s} | |
| 53 | 0110101 | {i,l,s,u} | |
| 54 | 0110110 | {i,l,s,t} | |
| 55 | 0110111 | {i,l,s,t,u} | |
| 56 | 0111000 | {i,l,r} | |
| 57 | 0111001 | {i,l,r,u} | |
| 58 | 0111010 | {i,l,r,t} | |
| 59 | 0111011 | {i,l,r,t,u} | |
| 60 | 0111100 | {i,l,r,s} | |
| 61 | 0111101 | {i,l,r,s,u} | |
| 62 | 0111110 | {i,l,r,s,t} | |
| 63 | 0111111 | {i,l,r,s,t,u} | |
| 64 | 1000000 | a, | {a} |
| 65 | 1000001 | a, | {a,u} |
| 66 | 1000010 | a, | {a,t} |
| 67 | 1000011 | a, | {a,t,u} |
| 68 | 1000100 | a, | {a,s} |
| 69 | 1000101 | a, | {a,s,u} |
| 70 | 1000110 | a, | {a,s,t} |
| 71 | 1000111 | a, | {a,s,t,u} |
| 72 | 1001000 | a, | {a,r} |
| 73 | 1001001 | a, | {a,r,u} |
| 74 | 1001010 | a, | {a,r,t} |
| 75 | 1001011 | a, | {a,r,t,u} |
| 76 | 1001100 | a, | {a,r,s} |
| 77 | 1001101 | a, | {a,r,s,u} |
| 78 | 1001110 | a, | {a,r,s,t} |
| 79 | 1001111 | a, | {a,r,s,t,u} |
| 80 | 1010000 | a, | {a,l} |
| 81 | 1010001 | a, | {a,l,u} |
| 82 | 1010010 | a, | {a,l,t} |
| 83 | 1010011 | a, | {a,l,t,u} |
| 84 | 1010100 | a, | {a,l,s} |
| 85 | 1010101 | a, | {a,l,s,u} |
| 86 | 1010110 | a, | {a,l,s,t} |
| 87 | 1010111 | a, | {a,l,s,t,u} |
| 88 | 1011000 | a, | {a,l,r} |
| 89 | 1011001 | a, | {a,l,r,u} |
| 90 | 1011010 | a, | {a,l,r,t} |
| 91 | 1011011 | a, | {a,l,r,t,u} |
| 92 | 1011100 | a, | {a,l,r,s} |
| 93 | 1011101 | a, | {a,l,r,s,u} |
| 94 | 1011110 | a, | {a,l,r,s,t} |
| 95 | 1011111 | a, | {a,l,r,s,t,u} |
| 96 | 1100000 | a,i, | {a,i} |
| 97 | 1100001 | a,i, | {a,i,u} |
| 98 | 1100010 | a,i, | {a,i,t} |
| 99 | 1100011 | a,i, | {a,i,t,u} |
| 100 | 1100100 | a,i, | {a,i,s} |
| 101 | 1100101 | a,i, | {a,i,s,u} |
| 102 | 1100110 | a,i, | {a,i,s,t} |
| 103 | 1100111 | a,i, | {a,i,s,t,u} |
| 104 | 1101000 | a,i, | {a,i,r} |
| 105 | 1101001 | a,i, | {a,i,r,u} |
| 106 | 1101010 | a,i, | {a,i,r,t} |
| 107 | 1101011 | a,i, | {a,i,r,t,u} |
| 108 | 1101100 | a,i, | {a,i,r,s} |
| 109 | 1101101 | a,i, | {a,i,r,s,u} |
| 110 | 1101110 | a,i, | {a,i,r,s,t} |
| 111 | 1101111 | a,i, | {a,i,r,s,t,u} |
| 112 | 1110000 | a,i,l, | {a,i,l} |
| 113 | 1110001 | a,i,l, | {a,i,l,u} |
| 114 | 1110010 | a,i,l, | {a,i,l,t} |
| 115 | 1110011 | a,i,l, | {a,i,l,t,u} |
| 116 | 1110100 | a,i,l, | {a,i,l,s} |
| 117 | 1110101 | a,i,l, | {a,i,l,s,u} |
| 118 | 1110110 | a,i,l, | {a,i,l,s,t} |
| 119 | 1110111 | a,i,l, | {a,i,l,s,t,u} |
| 120 | 1111000 | a,i,l,r, | {a,i,l,r} |
| 121 | 1111001 | a,i,l,r, | {a,i,l,r,u} |
| 122 | 1111010 | a,i,l,r, | {a,i,l,r,t} |
| 123 | 1111011 | a,i,l,r, | {a,i,l,r,t,u} |
| 124 | 1111100 | a,i,l,r,s, | {a,i,l,r,s} |
| 125 | 1111101 | a,i,l,r,s, | {a,i,l,r,s,u} |
| 126 | 1111110 | a,i,l,r,s,t, | {a,i,l,r,s,t} |
| 127 | 1111111 | a,i,l,r,s,t,u | {a,i,l,r,s,t,u} |
List our Power Set P in notation form:
Partition 1
{t,u},{a,i,l,r,s}
Partition 2
{t,u},{a,i,l,r,s}
Partition 3
{t,u},{a,i,l,r,s}
Partition 4
{t,u},{a,i,l,r,s}
Partition 5
{t,u},{a,i,l,r,s}
Partition 6
{s,u},
Partition 7
{s,u},
Partition 8
{s,u},
Partition 9
{s,u},
Partition 10
{s,u},
Partition 11
{s,t},
Partition 12
{s,t},
Partition 13
{s,t},
Partition 14
{s,t},
Partition 15
{s,t},
Partition 16
{s,t,u},{a,i,l,r}
Partition 17
{s,t,u},{a,i,l,r}
Partition 18
{s,t,u},{a,i,l,r}
Partition 19
{s,t,u},{a,i,l,r}
Partition 20
{r,u},{a,i,l,r,s}
Partition 21
{r,u},{a,i,l,r,s}
Partition 22
{r,u},{a,i,l,r,s}
Partition 23
{r,u},{a,i,l,r,s}
Partition 24
{r,u},{a,i,l,r,s}
Partition 25
{r,t},{a,i,l,r,s}
Partition 26
{r,t},{a,i,l,r,s}
Partition 27
{r,t},{a,i,l,r,s}
Partition 28
{r,t},{a,i,l,r,s}
Partition 29
{r,t},{a,i,l,r,s}
Partition 30
{r,t,u},
Partition 31
{r,t,u},
Partition 32
{r,t,u},
Partition 33
{r,t,u},
Partition 34
{r,s},
Partition 35
{r,s},
Partition 36
{r,s},
Partition 37
{r,s},
Partition 38
{r,s},
Partition 39
{r,s,u},
Partition 40
{r,s,u},
Partition 41
{r,s,u},
Partition 42
{r,s,u},
Partition 43
{r,s,t},
Partition 44
{r,s,t},
Partition 45
{r,s,t},
Partition 46
{r,s,t},
Partition 47
{r,s,t,u},{a,i,l}
Partition 48
{r,s,t,u},{a,i,l}
Partition 49
{r,s,t,u},{a,i,l}
Partition 50
{l,u},{a,i,l,r,s}
Partition 51
{l,u},{a,i,l,r,s}
Partition 52
{l,u},{a,i,l,r,s}
Partition 53
{l,u},{a,i,l,r,s}
Partition 54
{l,u},{a,i,l,r,s}
Partition 55
{l,t},{a,i,l,r,s}
Partition 56
{l,t},{a,i,l,r,s}
Partition 57
{l,t},{a,i,l,r,s}
Partition 58
{l,t},{a,i,l,r,s}
Partition 59
{l,t},{a,i,l,r,s}
Partition 60
{l,t,u},{a,i,l,r}
Partition 61
{l,t,u},{a,i,l,r}
Partition 62
{l,t,u},{a,i,l,r}
Partition 63
{l,t,u},{a,i,l,r}
Partition 64
{l,s},
Partition 65
{l,s},
Partition 66
{l,s},
Partition 67
{l,s},
Partition 68
{l,s},
Partition 69
{l,s,u},{a,i,l,r}
Partition 70
{l,s,u},{a,i,l,r}
Partition 71
{l,s,u},{a,i,l,r}
Partition 72
{l,s,u},{a,i,l,r}
Partition 73
{l,s,t},{a,i,l,r}
Partition 74
{l,s,t},{a,i,l,r}
Partition 75
{l,s,t},{a,i,l,r}
Partition 76
{l,s,t},{a,i,l,r}
Partition 77
{l,s,t,u},
Partition 78
{l,s,t,u},
Partition 79
{l,s,t,u},
Partition 80
{l,r},{a,i,l,r,s}
Partition 81
{l,r},{a,i,l,r,s}
Partition 82
{l,r},{a,i,l,r,s}
Partition 83
{l,r},{a,i,l,r,s}
Partition 84
{l,r},{a,i,l,r,s}
Partition 85
{l,r,u},
Partition 86
{l,r,u},
Partition 87
{l,r,u},
Partition 88
{l,r,u},
Partition 89
{l,r,t},
Partition 90
{l,r,t},
Partition 91
{l,r,t},
Partition 92
{l,r,t},
Partition 93
{l,r,t,u},
Partition 94
{l,r,t,u},
Partition 95
{l,r,t,u},
Partition 96
{l,r,s},
Partition 97
{l,r,s},
Partition 98
{l,r,s},
Partition 99
{l,r,s},
Partition 100
{l,r,s,u},
Partition 101
{l,r,s,u},
Partition 102
{l,r,s,u},
Partition 103
{l,r,s,t},
Partition 104
{l,r,s,t},
Partition 105
{l,r,s,t},
Partition 106
{l,r,s,t,u},{a,i}
Partition 107
{l,r,s,t,u},{a,i}
Partition 108
{i,u},{a,i,l,r,s}
Partition 109
{i,u},{a,i,l,r,s}
Partition 110
{i,u},{a,i,l,r,s}
Partition 111
{i,u},{a,i,l,r,s}
Partition 112
{i,u},{a,i,l,r,s}
Partition 113
{i,t},{a,i,l,r,s}
Partition 114
{i,t},{a,i,l,r,s}
Partition 115
{i,t},{a,i,l,r,s}
Partition 116
{i,t},{a,i,l,r,s}
Partition 117
{i,t},{a,i,l,r,s}
Partition 118
{i,t,u},{a,i,l,r}
Partition 119
{i,t,u},{a,i,l,r}
Partition 120
{i,t,u},{a,i,l,r}
Partition 121
{i,t,u},{a,i,l,r}
Partition 122
{i,s},
Partition 123
{i,s},
Partition 124
{i,s},
Partition 125
{i,s},
Partition 126
{i,s},
Partition 127
{i,s,u},{a,i,l,r}
Partition 128
{i,s,u},{a,i,l,r}
Partition 129
{i,s,u},{a,i,l,r}
Partition 130
{i,s,u},{a,i,l,r}
Partition 131
{i,s,t},{a,i,l,r}
Partition 132
{i,s,t},{a,i,l,r}
Partition 133
{i,s,t},{a,i,l,r}
Partition 134
{i,s,t},{a,i,l,r}
Partition 135
{i,s,t,u},{a,i,l}
Partition 136
{i,s,t,u},{a,i,l}
Partition 137
{i,s,t,u},{a,i,l}
Partition 138
{i,r},{a,i,l,r,s}
Partition 139
{i,r},{a,i,l,r,s}
Partition 140
{i,r},{a,i,l,r,s}
Partition 141
{i,r},{a,i,l,r,s}
Partition 142
{i,r},{a,i,l,r,s}
Partition 143
{i,r,u},
Partition 144
{i,r,u},
Partition 145
{i,r,u},
Partition 146
{i,r,u},
Partition 147
{i,r,t},
Partition 148
{i,r,t},
Partition 149
{i,r,t},
Partition 150
{i,r,t},
Partition 151
{i,r,t,u},{a,i,l}
Partition 152
{i,r,t,u},{a,i,l}
Partition 153
{i,r,t,u},{a,i,l}
Partition 154
{i,r,s},
Partition 155
{i,r,s},
Partition 156
{i,r,s},
Partition 157
{i,r,s},
Partition 158
{i,r,s,u},{a,i,l}
Partition 159
{i,r,s,u},{a,i,l}
Partition 160
{i,r,s,u},{a,i,l}
Partition 161
{i,r,s,t},{a,i,l}
Partition 162
{i,r,s,t},{a,i,l}
Partition 163
{i,r,s,t},{a,i,l}
Partition 164
{i,r,s,t,u},
Partition 165
{i,r,s,t,u},
Partition 166
{i,l},{a,i,l,r,s}
Partition 167
{i,l},{a,i,l,r,s}
Partition 168
{i,l},{a,i,l,r,s}
Partition 169
{i,l},{a,i,l,r,s}
Partition 170
{i,l},{a,i,l,r,s}
Partition 171
{i,l,u},{a,i,l,r}
Partition 172
{i,l,u},{a,i,l,r}
Partition 173
{i,l,u},{a,i,l,r}
Partition 174
{i,l,u},{a,i,l,r}
Partition 175
{i,l,t},{a,i,l,r}
Partition 176
{i,l,t},{a,i,l,r}
Partition 177
{i,l,t},{a,i,l,r}
Partition 178
{i,l,t},{a,i,l,r}
Partition 179
{i,l,t,u},
Partition 180
{i,l,t,u},
Partition 181
{i,l,t,u},
Partition 182
{i,l,s},{a,i,l,r}
Partition 183
{i,l,s},{a,i,l,r}
Partition 184
{i,l,s},{a,i,l,r}
Partition 185
{i,l,s},{a,i,l,r}
Partition 186
{i,l,s,u},
Partition 187
{i,l,s,u},
Partition 188
{i,l,s,u},
Partition 189
{i,l,s,t},
Partition 190
{i,l,s,t},
Partition 191
{i,l,s,t},
Partition 192
{i,l,s,t,u},
Partition 193
{i,l,s,t,u},
Partition 194
{i,l,r},
Partition 195
{i,l,r},
Partition 196
{i,l,r},
Partition 197
{i,l,r},
Partition 198
{i,l,r,u},
Partition 199
{i,l,r,u},
Partition 200
{i,l,r,u},
Partition 201
{i,l,r,t},
Partition 202
{i,l,r,t},
Partition 203
{i,l,r,t},
Partition 204
{i,l,r,t,u},
Partition 205
{i,l,r,t,u},
Partition 206
{i,l,r,s},
Partition 207
{i,l,r,s},
Partition 208
{i,l,r,s},
Partition 209
{i,l,r,s,u},
Partition 210
{i,l,r,s,u},
Partition 211
{i,l,r,s,t},
Partition 212
{i,l,r,s,t},
Partition 213
{i,l,r,s,t,u},{a}
Partition 214
{a,u},{a,i,l,r,s}
Partition 215
{a,u},{a,i,l,r,s}
Partition 216
{a,u},{a,i,l,r,s}
Partition 217
{a,u},{a,i,l,r,s}
Partition 218
{a,u},{a,i,l,r,s}
Partition 219
{a,t},{a,i,l,r,s}
Partition 220
{a,t},{a,i,l,r,s}
Partition 221
{a,t},{a,i,l,r,s}
Partition 222
{a,t},{a,i,l,r,s}
Partition 223
{a,t},{a,i,l,r,s}
Partition 224
{a,t,u},{a,i,l,r}
Partition 225
{a,t,u},{a,i,l,r}
Partition 226
{a,t,u},{a,i,l,r}
Partition 227
{a,t,u},{a,i,l,r}
Partition 228
{a,s},
Partition 229
{a,s},
Partition 230
{a,s},
Partition 231
{a,s},
Partition 232
{a,s},
Partition 233
{a,s,u},{a,i,l,r}
Partition 234
{a,s,u},{a,i,l,r}
Partition 235
{a,s,u},{a,i,l,r}
Partition 236
{a,s,u},{a,i,l,r}
Partition 237
{a,s,t},{a,i,l,r}
Partition 238
{a,s,t},{a,i,l,r}
Partition 239
{a,s,t},{a,i,l,r}
Partition 240
{a,s,t},{a,i,l,r}
Partition 241
{a,s,t,u},{a,i,l}
Partition 242
{a,s,t,u},{a,i,l}
Partition 243
{a,s,t,u},{a,i,l}
Partition 244
{a,r},{a,i,l,r,s}
Partition 245
{a,r},{a,i,l,r,s}
Partition 246
{a,r},{a,i,l,r,s}
Partition 247
{a,r},{a,i,l,r,s}
Partition 248
{a,r},{a,i,l,r,s}
Partition 249
{a,r,u},
Partition 250
{a,r,u},
Partition 251
{a,r,u},
Partition 252
{a,r,u},
Partition 253
{a,r,t},
Partition 254
{a,r,t},
Partition 255
{a,r,t},
Partition 256
{a,r,t},
Partition 257
{a,r,t,u},{a,i,l}
Partition 258
{a,r,t,u},{a,i,l}
Partition 259
{a,r,t,u},{a,i,l}
Partition 260
{a,r,s},
Partition 261
{a,r,s},
Partition 262
{a,r,s},
Partition 263
{a,r,s},
Partition 264
{a,r,s,u},{a,i,l}
Partition 265
{a,r,s,u},{a,i,l}
Partition 266
{a,r,s,u},{a,i,l}
Partition 267
{a,r,s,t},{a,i,l}
Partition 268
{a,r,s,t},{a,i,l}
Partition 269
{a,r,s,t},{a,i,l}
Partition 270
{a,r,s,t,u},{a,i}
Partition 271
{a,r,s,t,u},{a,i}
Partition 272
{a,l},{a,i,l,r,s}
Partition 273
{a,l},{a,i,l,r,s}
Partition 274
{a,l},{a,i,l,r,s}
Partition 275
{a,l},{a,i,l,r,s}
Partition 276
{a,l},{a,i,l,r,s}
Partition 277
{a,l,u},{a,i,l,r}
Partition 278
{a,l,u},{a,i,l,r}
Partition 279
{a,l,u},{a,i,l,r}
Partition 280
{a,l,u},{a,i,l,r}
Partition 281
{a,l,t},{a,i,l,r}
Partition 282
{a,l,t},{a,i,l,r}
Partition 283
{a,l,t},{a,i,l,r}
Partition 284
{a,l,t},{a,i,l,r}
Partition 285
{a,l,t,u},
Partition 286
{a,l,t,u},
Partition 287
{a,l,t,u},
Partition 288
{a,l,s},{a,i,l,r}
Partition 289
{a,l,s},{a,i,l,r}
Partition 290
{a,l,s},{a,i,l,r}
Partition 291
{a,l,s},{a,i,l,r}
Partition 292
{a,l,s,u},
Partition 293
{a,l,s,u},
Partition 294
{a,l,s,u},
Partition 295
{a,l,s,t},
Partition 296
{a,l,s,t},
Partition 297
{a,l,s,t},
Partition 298
{a,l,s,t,u},{a,i}
Partition 299
{a,l,s,t,u},{a,i}
Partition 300
{a,l,r},
Partition 301
{a,l,r},
Partition 302
{a,l,r},
Partition 303
{a,l,r},
Partition 304
{a,l,r,u},
Partition 305
{a,l,r,u},
Partition 306
{a,l,r,u},
Partition 307
{a,l,r,t},
Partition 308
{a,l,r,t},
Partition 309
{a,l,r,t},
Partition 310
{a,l,r,t,u},{a,i}
Partition 311
{a,l,r,t,u},{a,i}
Partition 312
{a,l,r,s},
Partition 313
{a,l,r,s},
Partition 314
{a,l,r,s},
Partition 315
{a,l,r,s,u},{a,i}
Partition 316
{a,l,r,s,u},{a,i}
Partition 317
{a,l,r,s,t},{a,i}
Partition 318
{a,l,r,s,t},{a,i}
Partition 319
{a,l,r,s,t,u},
Partition 320
{a,i},{a,i,l,r,s}
Partition 321
{a,i},{a,i,l,r,s}
Partition 322
{a,i},{a,i,l,r,s}
Partition 323
{a,i},{a,i,l,r,s}
Partition 324
{a,i},{a,i,l,r,s}
Partition 325
{a,i,u},{a,i,l,r}
Partition 326
{a,i,u},{a,i,l,r}
Partition 327
{a,i,u},{a,i,l,r}
Partition 328
{a,i,u},{a,i,l,r}
Partition 329
{a,i,t},{a,i,l,r}
Partition 330
{a,i,t},{a,i,l,r}
Partition 331
{a,i,t},{a,i,l,r}
Partition 332
{a,i,t},{a,i,l,r}
Partition 333
{a,i,t,u},{a,i,l}
Partition 334
{a,i,t,u},{a,i,l}
Partition 335
{a,i,t,u},{a,i,l}
Partition 336
{a,i,s},{a,i,l,r}
Partition 337
{a,i,s},{a,i,l,r}
Partition 338
{a,i,s},{a,i,l,r}
Partition 339
{a,i,s},{a,i,l,r}
Partition 340
{a,i,s,u},{a,i,l}
Partition 341
{a,i,s,u},{a,i,l}
Partition 342
{a,i,s,u},{a,i,l}
Partition 343
{a,i,s,t},{a,i,l}
Partition 344
{a,i,s,t},{a,i,l}
Partition 345
{a,i,s,t},{a,i,l}
Partition 346
{a,i,s,t,u},
Partition 347
{a,i,s,t,u},
Partition 348
{a,i,r},
Partition 349
{a,i,r},
Partition 350
{a,i,r},
Partition 351
{a,i,r},
Partition 352
{a,i,r,u},{a,i,l}
Partition 353
{a,i,r,u},{a,i,l}
Partition 354
{a,i,r,u},{a,i,l}
Partition 355
{a,i,r,t},{a,i,l}
Partition 356
{a,i,r,t},{a,i,l}
Partition 357
{a,i,r,t},{a,i,l}
Partition 358
{a,i,r,t,u},
Partition 359
{a,i,r,t,u},
Partition 360
{a,i,r,s},{a,i,l}
Partition 361
{a,i,r,s},{a,i,l}
Partition 362
{a,i,r,s},{a,i,l}
Partition 363
{a,i,r,s,u},
Partition 364
{a,i,r,s,u},
Partition 365
{a,i,r,s,t},
Partition 366
{a,i,r,s,t},
Partition 367
{a,i,r,s,t,u},
Partition 368
{a,i,l},{a,i,l,r}
Partition 369
{a,i,l},{a,i,l,r}
Partition 370
{a,i,l},{a,i,l,r}
Partition 371
{a,i,l},{a,i,l,r}
Partition 372
{a,i,l,u},
Partition 373
{a,i,l,u},
Partition 374
{a,i,l,u},
Partition 375
{a,i,l,t},
Partition 376
{a,i,l,t},
Partition 377
{a,i,l,t},
Partition 378
{a,i,l,t,u},
Partition 379
{a,i,l,t,u},
Partition 380
{a,i,l,s},
Partition 381
{a,i,l,s},
Partition 382
{a,i,l,s},
Partition 383
{a,i,l,s,u},
Partition 384
{a,i,l,s,u},
Partition 385
{a,i,l,s,t},
Partition 386
{a,i,l,s,t},
Partition 387
{a,i,l,s,t,u},
Partition 388
{a,i,l,r},
Partition 389
{a,i,l,r},
Partition 390
{a,i,l,r},
Partition 391
{a,i,l,r,u},
Partition 392
{a,i,l,r,u},
Partition 393
{a,i,l,r,t},
Partition 394
{a,i,l,r,t},
Partition 395
{a,i,l,r,t,u},
Partition 396
{a,i,l,r,s},
Partition 397
{a,i,l,r,s},
Partition 398
{a,i,l,r,s,u},
Partition 399
{a,i,l,r,s,t},
Partition 400
{{a},{i},{l},{r},{s},{t},{u})
What is the Answer?
How does the Power Sets and Set Partitions Calculator work?
This calculator has 1 input.
What 1 formula is used for the Power Sets and Set Partitions Calculator?
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
