Let \(S=(1,2,+\(ldots+12\)) and \(T_1,T_2+\(ldots+T_a\).

Printable View

- Mar 14th 2013, 07:15 AMgeniusgarvilSly Subsets of S
Let \(S=(1,2,+\(ldots+12\)) and \(T_1,T_2+\(ldots+T_a\).

- Mar 14th 2013, 07:24 AMHallsofIvyRe: Sly Subsets of S
I think you intended $\displaystyle S= (1, 2, +(\ldots+ 12))$ and $\displaystyle (T_1, T_2+ (\ldots+ T_a))$

but I have no idea what thatis supposed to mean! I think those are intended to be sets but what does the "+" mean? And what are you trying to say about them? - Mar 17th 2013, 12:21 AMgeniusgarvilRe: Sly Subsets of S
Actually, the question goes like this.

Let S={1,2,3,…12} and T1,T2,…Ta be subsets of S such that Ti⊄Tj∀i≠j. What is the maximum possible value of a? - Mar 17th 2013, 03:44 AMPlatoRe: Sly Subsets of S

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 $\displaystyle T_a\subseteq T$ but says nothing about how $\displaystyle T_a\text{ nor }T$.

I personally have never the term $\displaystyle Sly$. Please define. - Mar 17th 2013, 06:26 AMgeniusgarvilRe: Sly Subsets of S
As i have mentioned the complete question,and also clearly mentioned that T1,T2,.... Ta are subsets of S, if u are not able to solve it , u are not allowed to criticize me.

- Mar 17th 2013, 06:38 AMPlatoRe: Sly Subsets of S
**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 $\displaystyle T_1,T_2,\cdots, T_a$ are subsets of $\displaystyle S$", tells us nothing whatsoever about their properties.

No one can help with a totally unreadable question. - Mar 17th 2013, 02:49 PMmajaminRe: Sly Subsets of S
Let T be a collection of sets $\displaystyle T_i$ 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 $\displaystyle T_{(k)}$ to be a collection of subsets of size k (for which no two are subsets of each other). Then in this case, $\displaystyle |T_{(6)}| = {12 \choose 6} = 924$ 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 $\displaystyle T_i$ of size n that we include in our set T, we cannot include $\displaystyle {12 \choose (n-1)}$ subsets in our collection (this would violate the condition Ti⊄Tj above). Specifically, if we introduced a larger set in $\displaystyle T_{(6)}$ to make it "bigger" it would necessarily be a superset to a subset in $\displaystyle T_{(6)}$ (hence violating the condition).

- Mar 17th 2013, 04:18 PMPlatoRe: Sly Subsets of S
@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?" - Mar 17th 2013, 06:02 PMmajaminRe: Sly Subsets of S