Let \(S=(1,2,+\(ldots+12\)) and \(T_1,T_2+\(ldots+T_a\).
As written, that post really has no clear meaning. I suspect you are using some sort of translation program.
Moreover, this must be part of a larger question. You should post the whole question.
It says that but says nothing about how .
I personally have never the term . Please define.
No one criticized you.
The posted question is unreadable in English.
It does not define very essential parts of the question.
The fact that it "clearly mentioned that are subsets of ", tells us nothing whatsoever about their properties.
No one can help with a totally unreadable question.
Let T be a collection of sets for which Ti⊄Tj∀i≠j. If two different subsets have the same cardinality they are only subsets of each other iff they are equal. Define to be a collection of subsets of size k (for which no two are subsets of each other). Then in this case, is a maximum for sets of equal size (you can verify that sets of smaller size give a smaller collection). Now, suppose that we "mix" sets of different sizes to attain a larger number. For every set of size n that we include in our set T, we cannot include subsets in our collection (this would violate the condition Ti⊄Tj above). Specifically, if we introduced a larger set in to make it "bigger" it would necessarily be a superset to a subset in (hence violating the condition).
@majamin, that answer makes perfect sense. But how did you get that from tbhe other postings?
@geniusgarvil, I understand that you may have a language problem, a translation problem.
But if majamin read your question correctly, why in the world did you not post it clearly?
"What is the maximal number of subsets of S that no two have the property that neither is a subset of the other?"