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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

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 93E
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Prove the first absorption law from Table 1 by showing that if A and B are sets, then A ∪ (A ∩ 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
Transcribed Image Text: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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