Which of the following relations E are equivalence relations on the set of integers Z? a. xEy if and only if x - y is an even integer. b. xEy if and only if x- y is an odd integer. c. xEy if and only if x < y.

Which of the following relations E are equivalence relations on the set of integers Z? a. xEy if and only if x - y is an even integer. b. xEy if and only if x- y is an odd integer. c. xEy if and only if x < y.

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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3.
Which of the following relations E are equivalence relations on the set of
integers Z?
a. xEy if and only if x – y is an even integer.
b. xEy if and only if x – y is an odd integer.
c. xEy if and only if x < y.
d. xEy if and only if x divides y.
e. xEy if and only if x2 = y2.
f. xEy if and only if |x| = lyl.
g. xEy if and only if |x – y| < 2.

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