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The domain for the relation R is the set of all integers. For any two integers, x and y, xRy 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 al integers, not just positive integers.) Symmetric Transitive Anti-symmetric

The domain for the relation R is the set of all integers. For any two integers, x and y, xRy 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 al integers, not just positive integers.) Symmetric Transitive Anti-symmetric

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Understanding Relations on the Set of Integers** The domain for the relation \( R \) is the set of all integers. For any two integers, \( x \) and \( y \), \( xRy \) 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.) Please select which properties the relation \( R \) satisfies: - [ ] Symmetric - [ ] Transitive - [ ] Anti-symmetric - [ ] Reflexive **Definitions of Properties:** 1. **Symmetric:** A relation \( R \) on a set \( A \) is symmetric if, for every \( a \) and \( b \) in \( A \), whenever \( aRb \), then \( bRa \). 2. **Transitive:** A relation \( R \) on a set \( A \) is transitive if, for every \( a \), \( b \), and \( c \) in \( A \), whenever \( aRb \) and \( bRc \), then \( aRc \). 3. **Anti-symmetric:** A relation \( R \) on a set \( A \) is anti-symmetric if, for every \( a \) and \( b \) in \( A \), whenever \( aRb \) and \( bRa \), then \( a = b \). 4. **Reflexive:** A relation \( R \) on a set \( A \) is reflexive if, for every \( a \) in \( A \), the relation \( aRa \) holds. These properties will help in understanding the characteristics and behavior of the relation \( R \) applied to the set of all integers.
Transcribed Image Text:**Understanding Relations on the Set of Integers** The domain for the relation \( R \) is the set of all integers. For any two integers, \( x \) and \( y \), \( xRy \) 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.) Please select which properties the relation \( R \) satisfies: - [ ] Symmetric - [ ] Transitive - [ ] Anti-symmetric - [ ] Reflexive **Definitions of Properties:** 1. **Symmetric:** A relation \( R \) on a set \( A \) is symmetric if, for every \( a \) and \( b \) in \( A \), whenever \( aRb \), then \( bRa \). 2. **Transitive:** A relation \( R \) on a set \( A \) is transitive if, for every \( a \), \( b \), and \( c \) in \( A \), whenever \( aRb \) and \( bRc \), then \( aRc \). 3. **Anti-symmetric:** A relation \( R \) on a set \( A \) is anti-symmetric if, for every \( a \) and \( b \) in \( A \), whenever \( aRb \) and \( bRa \), then \( a = b \). 4. **Reflexive:** A relation \( R \) on a set \( A \) is reflexive if, for every \( a \) in \( A \), the relation \( aRa \) holds. These properties will help in understanding the characteristics and behavior of the relation \( R \) applied to the set of all integers.
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