Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C) has at least one member. Does it follow that A – (BnC) = (A – B) n (A –- C)? If so, prove that it does. If not, give a specific example to show that it does not.

Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C) has at least one member. Does it follow that A – (BnC) = (A – B) n (A –- C)? If so, prove that it does. If not, give a specific example to show that it does not.

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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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C,
and (A – B) n (A – C) has at least one member. Does it follow that A – (BnC) =
(A – B) n (A – C)? If so, prove that it does. If not, give a specific example to show
that it does not.

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