Let's take two elements from different domains.
The first element f ∈ {a, b, c, d} and s ∈ in N
I also have a list of relationship between these elements which can be represented as it follows
+--------+--------+
| f | s |
+--------+--------+
| a | 1 |
+--------+--------+
| a | 2 |
+--------+--------+
| b | 1 |
+--------+--------+
| b | 2 |
+--------+--------+
| c | 3 |
+--------+--------+
| d | 4 |
+--------+--------+
| d | 5 |
+--------+--------+
Two elements are in relationship if they are listed in that table on the same row. So for example a and 1 are related.
The scope is to partition the bigger set which contains {a, b, c, d, 1, 2, 3, 4, 5} in smaller sets which are
- mutually exclusive
- The union of all the partition sets must equal the initial set
- Each partition set must contain all the elements which are related together.
This means that it's acceptable to have 3 partitions like:
{a, b, 1, 2}, {c, 3}, {d, 4, 5}
But we cannot have
{a, b, 1}, {c, 2, 3}, {d, 4, 5}
Since a is related to 2 so they must be in the same set.
I would like to find one or more acceptable partitions. I found the solution manually but I couldn't get the theory which is leading to the solution.