A question states, " Let $S$ be an even set, $\{1,2,3,4....n\}$ such that $n>2$. Let $S_1,S_2,\dotsc,S_n$ be even subsets of $S$" This implies there has to be some order of listing the subsets. What is that order? Also, For an even set of $n$ members, there are $2^{n-1}$ even subsets.Then why is the last subset $S_n$?
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2What's an "even set", to begin with? – Hans Lundmark Dec 02 '17 at 11:09
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a set containing even no. of elements – satan 29 Dec 02 '17 at 11:14
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It's quite reasonable that you are puzzled, because this is a very badly-written question. – MJD Dec 02 '17 at 14:29
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now that I think about, the second part isn't wrong, it's just considering n subsets out of a total of 2^(n-1) possible even subsets. However, I still don't know what S1, S2, S3.... correspond to – satan 29 Dec 02 '17 at 14:40
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All you have told us is the hypothesis of a problem. We are given an even set $S={1,2,\dots,n}$ with $n\gt2$ and $n$ even subsets of $S$ labeled $S_1,S_2,\dots,S_n$. It would be interesting to know what we are supposed to prove or find from that. How about telling us the rest of the question? – bof Dec 02 '17 at 18:05
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prove there exists some i and j such that 1<j<_n and the intersection of Si and Sj is an even set – satan 29 Dec 03 '17 at 01:41
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I have an approach, – satan 29 Dec 03 '17 at 01:41
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if I can somehow prove Si and Sj are disjoint, then Their intersection will be the null set, which will be even. But then again, I Don't know what Si and Sj correspond to! – satan 29 Dec 03 '17 at 01:43