Which of the following define equivalence relations on the set Z-{0}? A/ a ~ b if and only if a2=b4. B/ ab if and only if both a,b are divisible by 3. C/ ab if and only if a,b have the same parity.
Which of the following define equivalence relations on the set Z-{0}? A/ a ~ b if and only if a2=b4. B/ ab if and only if both a,b are divisible by 3. C/ ab if and only if a,b have the same parity.
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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![Which of the following define equivalence
relations on the set Z-{0}?
A/ a ~ b if and only if a2=b4.
B/ ab if and only if both a,b are divisible
by 3.
C/ ab if and only if a,b have the same
parity.
D/ ab if and only if |a-5|=|b−5|.
E/ a~ b if and only if y(a)=([b]), where
is the Euler-up function.
F/ ab if and only if |a|, |b| are coprime.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafdbb166-7cb3-4c56-8458-138a9c466689%2F534f4a31-88b9-4064-a253-d712f392d152%2Fw2bs5ql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Which of the following define equivalence
relations on the set Z-{0}?
A/ a ~ b if and only if a2=b4.
B/ ab if and only if both a,b are divisible
by 3.
C/ ab if and only if a,b have the same
parity.
D/ ab if and only if |a-5|=|b−5|.
E/ a~ b if and only if y(a)=([b]), where
is the Euler-up function.
F/ ab if and only if |a|, |b| are coprime.
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