**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.

Answer: The domain of relation D is the set of positive integers. For x, y ∈ Z+, xDy if x evenly…

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)

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Author:James Kurose, Keith Ross

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Chapter1: Computer Networks And The Internet

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Question

**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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