A community for students.
Here's the question you clicked on:
 0 viewing
vishal_kothari
 4 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
vishal_kothari
 4 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

This Question is Closed

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

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.1It 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
 4 years ago
Best ResponseYou've already chosen the best response.1i m confused too....

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.1Could we just let \(A = \emptyset \) ? Then \(A* = \emptyset\) and since the empty set is contained in every set, the claim is true.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.