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(c) The domain of relation P is the set of all positive integers. For x, y e Z*, XPy if there is a positive integer n such that x" = y. (0) The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) The domain for the relation A is the set of all real numbers. xAy if |x - y| < 2.

(c) The domain of relation P is the set of all positive integers. For x, y e Z*, XPy if there is a positive integer n such that x" = y. (0) The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) The domain for the relation A is the set of all real numbers. xAy if |x - y| < 2.

Advanced Engineering Mathematics
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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Question

For each relation, indicate whether the relation is:

  • reflexive, anti-reflexive, or neither
  • symmetric, anti-symmetric, or neither
  • transitive or not transitive
(c) The domain of relation P is the set of all positive integers. For x, y e Z*, xPy if there is a positive integer n such that x" = y. (0) The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) (e) The domain for the relation A is the set of all real numbers. XAy if |x - yl s 2.
Transcribed Image Text:(c) The domain of relation P is the set of all positive integers. For x, y e Z*, xPy if there is a positive integer n such that x" = y. (0) The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) (e) The domain for the relation A is the set of all real numbers. XAy if |x - yl s 2.
Expert Solution
Step 1

c Reflexive: Let x∈Z+

there is a positive integer 1 such that  x1=x

⇒xPx 

⇒ Relation is reflexive.

Symmetric: Let x,y∈Z+ and xPy

since xPy⇒ there exist a positive integer such that xn=y

⇒x=y1n

since 1n∉N 

⇒yPx

⇒ Relation is not symmetric.

 

 

 

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