vishal_kothari
  • vishal_kothari
Suppose that for every (including the empty set and the whole set) subset X of a finite set S there is a subset X∗ of S and suppose that if X is a subset of Y then X∗ is a subset of Y∗ . Show that there is a subset A of S satisfying A∗ = A
Mathematics
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SOLVED
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katieb
  • katieb
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KingGeorge
  • KingGeorge
Hold on, I'm getting confused here.
KingGeorge
  • KingGeorge
It says that "for every subset \(X \subseteq S\) there is a subset \(X* \subseteq S\). Thus, if \(A \subseteq S\) then \(A* \subseteq S\). We also know by the second hypothesis that \(A* \subseteq S*\). But this is basically just restating the hypotheses.
vishal_kothari
  • vishal_kothari
i m confused too....

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KingGeorge
  • KingGeorge
Could we just let \(A = \emptyset \) ? Then \(A* = \emptyset\) and since the empty set is contained in every set, the claim is true.

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