TABLE 1 Set Identities. Identity Name AnU = A Identity laws AUØ = A AUU = U AnØ = Ø Domination laws AUA = A AnA = A Idempotent laws (A) = A Complementation law AUB = BUA Commutative laws AnB = BOA AU (BU C) = (A U B) U C An (Bn C) = (A n B)nC Associative laws AU (Bn C) = (A U B) n (A U C) An (BU C) = (A n B) U (An C) Distributive laws AOB = AUB AUB = AnB De Morgan's laws AU (An B) = A Absorption laws An (AU B) = A AUĀ = U A NĀ= Ø Complement laws

TABLE 1 Set Identities. Identity Name AnU = A Identity laws AUØ = A AUU = U AnØ = Ø Domination laws AUA = A AnA = A Idempotent laws (A) = A Complementation law AUB = BUA Commutative laws AnB = BOA AU (BU C) = (A U B) U C An (Bn C) = (A n B)nC Associative laws AU (Bn C) = (A U B) n (A U C) An (BU C) = (A n B) U (An C) Distributive laws AOB = AUB AUB = AnB De Morgan's laws AU (An B) = A Absorption laws An (AU B) = A AUĀ = U A NĀ= Ø Complement laws

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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Concept explainers

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

Prove the domination laws in Table 1 by showing that
a) A ∪ U = U. b) A ∩ ∅ = ∅.

TABLE 1 Set Identities.
Identity
Name
AnU = A
Identity laws
AUØ = A
AUU = U
AnØ = Ø
Domination laws
AUA = A
AnA = A
Idempotent laws
(A) = A
Complementation law
AUB = BUA
Commutative laws
AnB = BOA
AU (BU C) = (A U B) U C
An (Bn C) = (A n B)nC
Associative laws
AU (Bn C) = (A U B) n (A U C)
An (BU C) = (A n B) U (An C)
Distributive laws
AOB = AUB
AUB = AnB
De Morgan's laws
AU (An B) = A
Absorption laws
An (AU B) = A
AUĀ = U
A NĀ= Ø
Complement laws

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