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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
 2 years ago
 2 years ago
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
 2 years ago
 2 years ago

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KingGeorgeBest ResponseYou've already chosen the best response.1
Hold on, I'm getting confused here.
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.1
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.
 2 years ago

vishal_kothariBest ResponseYou've already chosen the best response.1
i m confused too....
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Could we just let \(A = \emptyset \) ? Then \(A* = \emptyset\) and since the empty set is contained in every set, the claim is true.
 2 years ago
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