Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
c. Ris a relation on Z such that (x, y) e R if and only if xy 2 0. d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n such that x" = y. e. Ris a relation on R such that (x, y) ER if and only if x – y is rational. Hint: The sum of two rational numbers is rational.

c. Ris a relation on Z such that (x, y) e R if and only if xy 2 0. d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n such that x" = y. e. Ris a relation on R such that (x, y) ER if and only if x – y is rational. Hint: The sum of two rational numbers is rational.

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
See similar textbooks
icon
Related questions
Question

Solve C, D, E please and Thankyou.

### Relations and Their Properties For each of the following relations, determine whether the relation is: - **Reflexive** - **Anti-reflexive** - **Symmetric** - **Anti-symmetric** - **Transitive** - **A partial order** - **A strict order** - **An equivalence relation** **Justify all your answers.** #### a. Relation on People **Description:** \( R \) is a relation on the set of all people such that \((a, b) \in R\) if and only if \(a\) and \(b\) have a common grandparent. #### b. Relation on Power Sets **Description:** \( R \) is a relation on the power set of a set \( A \) such that \((X, Y) \in R\) if and only if \( X \subseteq Y \). #### c. Relation on Integers \( \mathbb{Z} \) **Description:** \( R \) is a relation on \( \mathbb{Z} \) such that \((x, y) \in R\) if and only if \( xy \geq 0 \). #### d. Relation on Positive Integers \( \mathbb{Z}^+ \) **Description:** \( R \) is a relation on \( \mathbb{Z}^+ \) such that \((x, y) \in R\) if and only if there is a positive integer \( n \) such that \( x^n = y \). #### e. Relation on Real Numbers \( \mathbb{R} \) **Description:** \( R \) is a relation on \( \mathbb{R} \) such that \((x, y) \in R\) if and only if \( x - y \) is rational. **Hint:** The sum of two rational numbers is rational.
Transcribed Image Text:### Relations and Their Properties For each of the following relations, determine whether the relation is: - **Reflexive** - **Anti-reflexive** - **Symmetric** - **Anti-symmetric** - **Transitive** - **A partial order** - **A strict order** - **An equivalence relation** **Justify all your answers.** #### a. Relation on People **Description:** \( R \) is a relation on the set of all people such that \((a, b) \in R\) if and only if \(a\) and \(b\) have a common grandparent. #### b. Relation on Power Sets **Description:** \( R \) is a relation on the power set of a set \( A \) such that \((X, Y) \in R\) if and only if \( X \subseteq Y \). #### c. Relation on Integers \( \mathbb{Z} \) **Description:** \( R \) is a relation on \( \mathbb{Z} \) such that \((x, y) \in R\) if and only if \( xy \geq 0 \). #### d. Relation on Positive Integers \( \mathbb{Z}^+ \) **Description:** \( R \) is a relation on \( \mathbb{Z}^+ \) such that \((x, y) \in R\) if and only if there is a positive integer \( n \) such that \( x^n = y \). #### e. Relation on Real Numbers \( \mathbb{R} \) **Description:** \( R \) is a relation on \( \mathbb{R} \) such that \((x, y) \in R\) if and only if \( x - y \) is rational. **Hint:** The sum of two rational numbers is rational.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS