Theorem (Axioms of a Derived set): Let (M,d) be a metric space and let S,T C M. Then(1) S ST = S' ST".(2) (SUT)' = S'UT'.(3) In general, (S n T)' S s'nT', but (SsnT)' S'nT'.(4) S = S'US.

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 21E

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Theorem (Axioms of a Derived set): Let (M,d) be a metric space and let S,T C M. Then (1) S CT S' S T'. (4) 5 = S'US. (2) (SUT)' = S'U T". (3) In general, (S n T)' S s'nT', but (S nT)' # S'nT.