26 DQuestion 26Table 3.5.1: Set identities.NameIdempotent lawsAssociative lawsCommutative lawsDistributive lawsIdentity lawsDomination lawsDouble complementlawComplement lawsDe Morgan's lawsAbsorption lawsAUA-A(AUB) UC-AU (BUC)AUB-BUAAU (BNC)=(AUB) n(AuAUG-AANØ ØAnA=0U ØIdentitiesAUB ANBAU (ANB)-AΑΓΑ-Α(ANB) nc-An (BNC)ANB-BOAAn (BUC)-(ANB) U (ANC)ANU-AAUU-UA -AAUA-U0=UANB-AUBAn (AUB)-AThe set subtraction law states that A - B = An B.Use the set subtraction law as well as the other set identities given in the tableabove to prove each of the following new identity.Label each step in your proof with the set identity used to establish that step.Prove: A-(BA) = A - B

Given identity is, A-(B∩A)=A-B It contains two sets A, B.

Table 3.5.1: Set identities. Name Idempotent laws Associative laws Commutative laws Distributive laws Identity laws Domination laws Double complement law Complement laws De Morgan's laws Absorption laws AUA-A (AUB) UC-AU (BUC) AUB-BUA Identities AU (BOC)-(AUB) n (AU (C)=(A AUØ-A ANGIO AnA=0 UIØ AUB-ANB AU (ANB)-A ΑΠΑΞΑ (ANB) NC-An (BNC) ANB-BNA An (Buc)-(ANB) u (AN C) ANU-A AUU-U A -A AUA-U O=U ANB-AUB AN (AUB)-A The set subtraction law states that A - B = An B. Use the set subtraction law as well as the other set identities given in the table above to prove each of the following new identity. Label each step in your proof with the set identity used to establish that step. Prove: A-(BA) = A - B

Table 3.5.1: Set identities. Name Idempotent laws Associative laws Commutative laws Distributive laws Identity laws Domination laws Double complement law Complement laws De Morgan's laws Absorption laws AUA-A (AUB) UC-AU (BUC) AUB-BUA Identities AU (BOC)-(AUB) n (AU (C)=(A AUØ-A ANGIO AnA=0 UIØ AUB-ANB AU (ANB)-A ΑΠΑΞΑ (ANB) NC-An (BNC) ANB-BNA An (Buc)-(ANB) u (AN C) ANU-A AUU-U A -A AUA-U O=U ANB-AUB AN (AUB)-A The set subtraction law states that A - B = An B. Use the set subtraction law as well as the other set identities given in the table above to prove each of the following new identity. Label each step in your proof with the set identity used to establish that step. Prove: A-(BA) = A - B

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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