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Consider the following statement. For all sets A and B, (A U BC) - B = (A - B) UBC. 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 (AUB)- B = (AUB)n BC = (BCn A) U (BC n BC) = (BCn A) U BC = (A - B) U BC by the set difference law by the distributive law by the idempotent law for U by the set difference law. The commutative law is needed between between steps (3) and (4). The absorption law is needed between steps (2) and (3). The double complement law is needed between steps (3) and (4). The complement law is needed between steps (2) and (3). The commutative law is needed between between steps (1) and (2). X (1) (2) (3) (4)

Consider the following statement. For all sets A and B, (A U BC) - B = (A - B) UBC. 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 (AUB)- B = (AUB)n BC = (BCn A) U (BC n BC) = (BCn A) U BC = (A - B) U BC by the set difference law by the distributive law by the idempotent law for U by the set difference law. The commutative law is needed between between steps (3) and (4). The absorption law is needed between steps (2) and (3). The double complement law is needed between steps (3) and (4). The complement law is needed between steps (2) and (3). The commutative law is needed between between steps (1) and (2). X (1) (2) (3) (4)

Advanced Engineering Mathematics
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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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.) 000 Let any sets A and B be given. Then (A U BC) - B = (A U BC) n BC = (BC n A) U (BC n BC) (BCn A) U BC = (A - B) U BC by the set difference law by the distributive law by the idempotent law for U by the set difference law The commutative law is needed between between steps (3) and (4). The absorption law is needed between steps (2) and (3). The double complement law is needed between steps (3) and (4). The complement law is needed between steps (2) and (3). The commutative law is needed between between steps (1) and (2). (1) (2) (3) (4)
Transcribed Image Text: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.) 000 Let any sets A and B be given. Then (A U BC) - B = (A U BC) n BC = (BC n A) U (BC n BC) (BCn A) U BC = (A - B) U BC by the set difference law by the distributive law by the idempotent law for U by the set difference law The commutative law is needed between between steps (3) and (4). The absorption law is needed between steps (2) and (3). The double complement law is needed between steps (3) and (4). The complement law is needed between steps (2) and (3). The commutative law is needed between between steps (1) and (2). (1) (2) (3) (4)
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