7. Show that Theorem 10.40 is best possible in the following sense. (a) There exist sets A,...

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7. Show that Theorem 10.40 is best possible in the following sense.

(a) There exist sets A, Bin R such that (A U B)O i A~ U BO.

(b) There exist sets A, B in R such that A n B =f A n B.

(c) There exist sets A, Bin R such that 8(A U B) =f 8A U 8B and 8(A n B) =f

(A n 8B) U (B n 8A) U (8A n 8B).

~. This exercise is used many times from Section 10.4 onward.

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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7. Show that Theorem 10.40 is best possible in the following sense. (a) There exist sets A,...

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An Introduction To Analysis

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