If.u=(a,b,c,d),list.all.possible.subsets.of.u
Thanks
a, ab, ac, ad, abc, abd, acd
b, bc, bd, bcd
c, cd
d
if not confining yourself to proper subsets, there's also
abcd and the empty set
To find all possible subsets of a set, you can use the power set concept. The power set of a set is the set of all possible subsets, including the empty set and the set itself.
In this case, you have the set u = (a, b, c, d). To find all the possible subsets of u, you can follow these steps:
1. Identify the number of elements in the set: In this case, u has four elements (a, b, c, and d).
2. Determine the total number of subsets: Since each element can either be included or excluded, the total number of subsets will be 2 raised to the power of the number of elements in the set.
In this case, there are 4 elements, so the total number of subsets will be 2^4 = 16 subsets.
3. Generate binary combinations: Convert the numbers from 0 to 15 (in binary form) into four-digit binary numbers with leading zeros if necessary. These binary numbers will represent the inclusion or exclusion of each element in the set.
0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
4. Map binary combinations to subsets: Each binary digit represents the inclusion or exclusion of a corresponding element in the set. For example, in the binary number 0101, the first and third elements are included, while the second and fourth elements are excluded. Use these binary combinations to create subsets of the original set.
Applying this logic, we can map the binary combinations to subsets of the set u:
0000 -> {} (Empty set)
0001 -> {d}
0010 -> {c}
0011 -> {c, d}
0100 -> {b}
0101 -> {b, d}
0110 -> {b, c}
0111 -> {b, c, d}
1000 -> {a}
1001 -> {a, d}
1010 -> {a, c}
1011 -> {a, c, d}
1100 -> {a, b}
1101 -> {a, b, d}
1110 -> {a, b, c}
1111 -> {a, b, c, d} (Original set u)
Thus, the list of all possible subsets of u is:
{}, {d}, {c}, {c, d}, {b}, {b, d}, {b, c}, {b, c, d}, {a}, {a, d}, {a, c}, {a, c, d}, {a, b}, {a, b, d}, {a, b, c}, {a, b, c, d}