Answered: Let A be a subset of X, and B be a…

Let A be a subset of X, and B be a subset of X, where X is a metric space. Show the intersection of (A and B) complement is a subset of A complement intersection B complement.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A.) Let A be a subset of X, and B be a subset of X, where X is a metric space. Show the intersection of (A and B) complement is a subset of A complement intersection B complement.

B.) Consider A =[3,7), B = (7,9] as a subset of R with the usual metric

d_R(x,y) = abs(x-y). Show A complement intersection B complement is not a subset of the intersection of (A and B) complement.

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