Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some integer s}. A Is A C B? (Provide a proof if the statement is true or a disproof if the statement is false.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 4E: Find the smallest integer in the given set. { and for some in } { and for some in }
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Define sets A and B as:
: {n E Z\n = 4r + 3 for some integer r}.
• B= {m E Z m = 4s – 1 for some integer s}.
A
Is A C B?
(Provide a proof if the statement is true or a disproof
if the statement is false.)
Transcribed Image Text:Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some integer s}. A Is A C B? (Provide a proof if the statement is true or a disproof if the statement is false.)
Prove the following:
For all sets A, B :
If BC A° then AÑ B = Ø.
Transcribed Image Text:Prove the following: For all sets A, B : If BC A° then AÑ B = Ø.
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