Which of the following relations E are equivalence relations on the set of integers Z? 3. 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| = ly]. g. xEy if and only if |x – yl < 2.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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please answer the d, e, f, and g
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.
Transcribed Image Text: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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