Define a relation R, on the set A = {0, 1, 2, 3} as follows. R5 = {(0, 0), (0, 1), (0, 2), (1, 2)} Is R, reflexive, symmetric, transitive, or none of these? (Select all that apply.) O Rg is reflexive. R5 O R, is symmetric. O Rg is transitive. O R, is neither reflexive, symmetric, nor transitive. Let C be the circle relation defined on the following set of real numbers. For every x, y E R, x C y A x² + y2 = 1. Which of the following is true for C? (Select all that apply.) C is reflexive. O Cis symmetric. O C is transitive. O C is neither reflexive, symmetric, nor transitive.
Define a relation R, on the set A = {0, 1, 2, 3} as follows. R5 = {(0, 0), (0, 1), (0, 2), (1, 2)} Is R, reflexive, symmetric, transitive, or none of these? (Select all that apply.) O Rg is reflexive. R5 O R, is symmetric. O Rg is transitive. O R, is neither reflexive, symmetric, nor transitive. Let C be the circle relation defined on the following set of real numbers. For every x, y E R, x C y A x² + y2 = 1. Which of the following is true for C? (Select all that apply.) C is reflexive. O Cis symmetric. O C is transitive. O C is neither reflexive, symmetric, nor transitive.
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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![Define a relation \( R_5 \) on the set \( A = \{0, 1, 2, 3\} \) as follows.
\[ R_5 = \{(0, 0), (0, 1), (0, 2), (1, 2)\} \]
Is \( R_5 \) reflexive, symmetric, transitive, or none of these? (Select all that apply.)
- [ ] \( R_5 \) is reflexive.
- [ ] \( R_5 \) is symmetric.
- [ ] \( R_5 \) is transitive.
- [ ] \( R_5 \) is neither reflexive, symmetric, nor transitive.
Let \( C \) be the circle relation defined on the following set of real numbers.
For every \( x, y \in \mathbb{R}, \, x \, C \, y \iff x^2 + y^2 = 1 \).
Which of the following is true for \( C \)? (Select all that apply.)
- [ ] \( C \) is reflexive.
- [ ] \( C \) is symmetric.
- [ ] \( C \) is transitive.
- [ ] \( C \) is neither reflexive, symmetric, nor transitive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07ee186d-d8e7-4d24-aee8-a2563a0309f2%2F33e7bd1a-87df-4b90-b7e4-3a085b04315a%2F644g8q9_processed.png&w=3840&q=75)
Transcribed Image Text:Define a relation \( R_5 \) on the set \( A = \{0, 1, 2, 3\} \) as follows.
\[ R_5 = \{(0, 0), (0, 1), (0, 2), (1, 2)\} \]
Is \( R_5 \) reflexive, symmetric, transitive, or none of these? (Select all that apply.)
- [ ] \( R_5 \) is reflexive.
- [ ] \( R_5 \) is symmetric.
- [ ] \( R_5 \) is transitive.
- [ ] \( R_5 \) is neither reflexive, symmetric, nor transitive.
Let \( C \) be the circle relation defined on the following set of real numbers.
For every \( x, y \in \mathbb{R}, \, x \, C \, y \iff x^2 + y^2 = 1 \).
Which of the following is true for \( C \)? (Select all that apply.)
- [ ] \( C \) is reflexive.
- [ ] \( C \) is symmetric.
- [ ] \( C \) is transitive.
- [ ] \( C \) is neither reflexive, symmetric, nor transitive.
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