I need help with the attached question, please. Consider the following statement.For all sets A and B, (A U BC) - B = (A - B) U 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 thatapply.)Let any sets A and B be given. Then(A U BC) - B = (AUB) NBC= (BCNA) U (BCNBC)(BCN A) U BC(A - B) U BC==by the set difference lawby the distributive lawby the idempotent law for Uby the set difference lawO The commutative law is needed between between steps (3) and (4).O The complement law is needed between steps (2) and (3).O The commutative law is needed between between steps (1) and (2).O The double complement law is needed between steps (3) and (4).The absorption law is needed between steps (2) and (3).X(1)(2)(3)(4)

Answered: Image /qna-images/answer/7c39434e-8260-4fae-ae5c-0ef715b04948.jpg

Consider the following statement. For all sets A and B, (A U BC) - B = (A - B)U 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.) Let any sets A and B be given. Then (A U BC) - B=(AUB)n BC = (BCNA) U (BCNBC) = (BCA) U BC = (AB) U BC by by the set difference law by the distributive law the idempotent law for U by the set difference law 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 commutative law is needed between between steps (1) and (2). O The double complement law is needed between steps (3) and (4). O The absorption law is needed between steps (2) and (3). X (1) (2) (3) (4)

Consider the following statement. For all sets A and B, (A U BC) - B = (A - B)U 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.) Let any sets A and B be given. Then (A U BC) - B=(AUB)n BC = (BCNA) U (BCNBC) = (BCA) U BC = (AB) U BC by by the set difference law by the distributive law the idempotent law for U by the set difference law 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 commutative law is needed between between steps (1) and (2). O The double complement law is needed between steps (3) and (4). O The absorption law is needed between steps (2) and (3). X (1) (2) (3) (4)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 8TFE

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