1/2 | 128% + Question 4. Let N be the set of positive integers and let be a relation on N defined as follows 3 Vx.YEN X ~y if and only if x ≤y. < Is the relation ~ reflexive? is it symmetric? is it transitive? Justify you answers. Questions 5. 2 Let Z be the set of integers and let R be a relation on Z defined as follows Vx,yez xRy if and only if 7 divides (x - y). Is the relation R an equivalence relation? If R is an equivalence relation describe its equivalence classes. Question 6. Let us consider the following relation, where R denotes the set of real numbers RC R x R defined by Vx,yeR XRy׳ = y4 Determine if the relation R is a function defined on its domain? Justify your answer. Q Search H 1 pri sc F30 home insert delete [ backspace lock enter CE 7
1/2 | 128% + Question 4. Let N be the set of positive integers and let be a relation on N defined as follows 3 Vx.YEN X ~y if and only if x ≤y. < Is the relation ~ reflexive? is it symmetric? is it transitive? Justify you answers. Questions 5. 2 Let Z be the set of integers and let R be a relation on Z defined as follows Vx,yez xRy if and only if 7 divides (x - y). Is the relation R an equivalence relation? If R is an equivalence relation describe its equivalence classes. Question 6. Let us consider the following relation, where R denotes the set of real numbers RC R x R defined by Vx,yeR XRy׳ = y4 Determine if the relation R is a function defined on its domain? Justify your answer. Q Search H 1 pri sc F30 home insert delete [ backspace lock enter CE 7
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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Do question 5 only
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Question 4.
Let N be the set of positive integers and let be a relation on N defined as follows
3
Vx.YEN X ~y if and only if x ≤y.
<
Is the relation ~ reflexive? is it symmetric? is it transitive? Justify you answers.
Questions 5.
2
Let Z be the set of integers and let R be a relation on Z defined as follows
Vx,yez xRy if and only if 7 divides (x - y).
Is the relation R an equivalence relation? If R is an equivalence relation describe its equivalence classes.
Question 6.
Let us consider the following relation, where R denotes the set of real numbers
RC R x R defined by Vx,yeR XRy׳ = y4
Determine if the relation R is a function defined on its domain? Justify your answer.
Q Search
H
1
pri sc
F30
home
insert
delete
[
backspace
lock
enter
CE
7
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