A = {x = Z | x= 6a + 1 for some a € Z} B = {y≤ Z | y = 126 + 7 for some b = Z} C = {z €Z|z= 12c5 for some c = Z}. (a) Disprove that AC B. (HINT: write the definition of “not a subet of” by negating the subset defintion.) (b) Is BCA? Do not prove, but give reasons for your answer. (c) Use the "element chasing" method to prove that B = C;
A = {x = Z | x= 6a + 1 for some a € Z} B = {y≤ Z | y = 126 + 7 for some b = Z} C = {z €Z|z= 12c5 for some c = Z}. (a) Disprove that AC B. (HINT: write the definition of “not a subet of” by negating the subset defintion.) (b) Is BCA? Do not prove, but give reasons for your answer. (c) Use the "element chasing" method to prove that B = C;
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 16E: 16. Let and define on by if and only if . Determine whether is reflexive, symmetric, or...
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![A = {x ≤ Z | x = 6a + 1 for some a € Z}
B = {y = Z | y = 12b + 7 for some b = Z}
C = {z € Z | z = 12c5 for some c € Z}.
(a) Disprove that A C B.
(HINT: write the definition of “not a subet of” by negating the subset defintion.)
(b) Is BCA? Do not prove, but give reasons for your answer.
(c) Use the "element chasing" method to prove that B = C;](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98f7a83c-5485-4b59-b870-bc9d699336aa%2F14912b57-fe43-4134-a4a9-409dadcc028f%2Fc98imj2n_processed.png&w=3840&q=75)
Transcribed Image Text:A = {x ≤ Z | x = 6a + 1 for some a € Z}
B = {y = Z | y = 12b + 7 for some b = Z}
C = {z € Z | z = 12c5 for some c € Z}.
(a) Disprove that A C B.
(HINT: write the definition of “not a subet of” by negating the subset defintion.)
(b) Is BCA? Do not prove, but give reasons for your answer.
(c) Use the "element chasing" method to prove that B = C;
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