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Consider the following statement. For all sets A and B,  (A ∪ Bc) − B = (A − B) ∪ Bc. An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing. (Select all that apply.

Consider the following statement. For all sets A and B,  (A ∪ Bc) − B = (A − B) ∪ Bc. An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing. (Select all that apply.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 11E: For the sets gives in Exercise 9, is there a distributive relationship for union with respect with...
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Consider the following statement.
For all sets A and B, 
(A ∪ Bc) − B = (A − B) ∪ Bc.
An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing. (Select all that apply.)
Consider the following statement. For all sets A and B, (A U B) - B = (A – B) U Bº. An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing. (Select all that apply.) Let any sets A and B be given. Then (A U BC) – B = (A U B) N BC (Bº N A) U (Bº N Bº) = (BC N A) U Bc = (A – B) U Bc by the set difference law (1) by the distributive law (2) by the idempotent law for U (3) by the set difference law (4) V The absorption law is needed between steps (2) and (3). O The commutative law is needed between between steps (1) and (2). O The commutative law is needed between between steps (3) and (4). O The complement law is needed between steps (2) and (3). O The double complement law is needed between steps (3) and (4).
Transcribed Image Text:Consider the following statement. For all sets A and B, (A U B) - B = (A – B) U Bº. An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing. (Select all that apply.) Let any sets A and B be given. Then (A U BC) – B = (A U B) N BC (Bº N A) U (Bº N Bº) = (BC N A) U Bc = (A – B) U Bc by the set difference law (1) by the distributive law (2) by the idempotent law for U (3) by the set difference law (4) V The absorption law is needed between steps (2) and (3). O The commutative law is needed between between steps (1) and (2). O The commutative law is needed between between steps (3) and (4). O The complement law is needed between steps (2) and (3). O The double complement law is needed between steps (3) and (4).
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