I can draw Venn diagrams but now my question is more complicated than just drawing Venn diagrams one by one. I need to draw all possible Venn diagrams efficiently. I need a combinatorical approach because there are 256 combinations.
Let's choose the following sets as the case to consider. The binary number labels are used to uniquely identified each "atomic" region. My definition: An atomic region does not contain any smaller region.
Because there are 8 atomic regions, each can be either selected or not to compose a new compound region. Therefore there are 2^8 ways.
How to generate all possible Venn diagrams (with the case above) efficiently?
The objective is to produce 256 Venn diagrams, each diagram has a unique colored compound region that has an associated set operation.
Let's use 8-bit integer to represent each diagram.
The first bit (the most left bit or the most significant bit) represents the region
The second bit represents the region
The least significant bit represents the region
0 represent not-join to produce a new compound region. And
If the first diagram with the complement of
AuBuC then its binary representation is
1111 1111 represents
S. Etc etc etc!
The Problem Sheet
The problem sheet will ask the student to find a set operation (not necessarily unique) for each RED COMPOUND region in each diagram below.