I was looking for some sort of generalization on set operations between different sets, and how that number of operations increases as the number of set increase as well. It can also be thought as the number of sets represented in a Venn diagram of n sets. I'm not really sure how to put this into words so i think an example could be more clear.
Number of sets 2, let them be $A$ and $B$, then you have the following set operations in the Venn diagram: $A\cap B, A\cup B, A - B $ and $B - A$
If the number of sets is 3, $A, B$ and $C$, you will have: $A-(B \cup C)$, $(A \cap C)-B$, $B-(A \cup C)$, $A \cap B \cap C$, $(A \cap C) - B$, $(B \cap C) - A,$ $C -(A \cup B)$ and their complements.
If the number of set is 4: $A, B, C$, and $D$: $A - (B \cup D \cup C)$, $(A \cap B) - (D \cup C)$, $B - (A \cup D \cup C)$, $D - (A \cup B \cup C)$, $(B \cap D) - (A \cup C)$, $(A \cap D \cap B) - C$, $(A \cap D) - (B \cup C)$, $(D \cap C \cap A) - B$, $A \cap B \cap D \cap C$, $(D \cap B \cap C) - A$, $(D \cap C) - (A \cup B)$, $C - (A \cup B \cup D)$, $(C \cap B) -(A \cup D)$, $(A \cap B \cap C) - D$, $(A \cap C)-(B \cup D)$ and their complements.
I'm not sure if this a set theory problem or a combinatory problem, but I would like to know a way to generalize this to obtain the possible combinations of operations between sets a little bit larger, like 6, 8 or 10. to be able to compare the different elements present in those sets.
What you're looking for is the number of Boolean functions (aka truth functions) of $n$ variables. Equivalently, the number of truth tables with $n$ variables and an arbitrary extra column for the value of the function.
The number of assignments of values to $n$ variables is $2^n$, so the number of truth functions is $2^{2^n}$.