Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. (a) {3} ≤ {−1, 1, 3, 5, 6, 9}. (b) {−3,−2,−1,0, 1, 2} = {x € R | − 3 ≤ x ≤ 2}. (c) {6, {6}, (√6)²} ≤ {6, {6}, {{6}}}. (d) If A = {1,2,3,4} and B = {−1, 0, 1, 2, 3}, then any relation F from A to B contains exactly four ordered pairs. (e) {y € Z | 0 ≤ y ≤ 5} C {z €R | − 3 < z < 5}.
Answer TRUE or FALSE for each of (a)-(e). No justification is required for this problem. (a) {3} ≤ {−1, 1, 3, 5, 6, 9}. (b) {−3,−2,−1,0, 1, 2} = {x € R | − 3 ≤ x ≤ 2}. (c) {6, {6}, (√6)²} ≤ {6, {6}, {{6}}}. (d) If A = {1,2,3,4} and B = {−1, 0, 1, 2, 3}, then any relation F from A to B contains exactly four ordered pairs. (e) {y € Z | 0 ≤ y ≤ 5} C {z €R | − 3 < z < 5}.
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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![### Set Theory and Relations: True or False Questions
**Instructions:**
Answer TRUE or FALSE for each of the following statements (a)-(e). Justifications are not required for this problem.
---
**(a) Subsets**
Is the set \(\{3\}\) a subset of the set \(\{-1, 1, 3, 5, 6, 9\}\)?
\[\{3\} \subseteq \{-1, 1, 3, 5, 6, 9\}.\]
---
**(b) Interval Notation and Set Membership**
Does the set \(\{-3, -2, -1, 0, 1, 2\}\) equal the set of real numbers \(x\) that satisfy \(-3 \leq x \leq 2\)?
\[\{-3, -2, -1, 0, 1, 2\} = \{x \in \mathbb{R} \mid -3 \leq x \leq 2\}.\]
---
**(c) Set Inclusion and Square Roots**
Is the set containing \(6\), the set containing \(6\), and the square root of \(6\) squared a subset of the set containing \(6\), the set containing \(6\), and the set whose only element is the set containing \(6\)?
\[\{6, \{6\}, \left(\sqrt{6}\right)^2\} \subseteq \{6, \{6\}, \{\{6\}\}\}.\]
---
**(d) Relations Between Sets**
If \(A = \{1, 2, 3, 4\}\) and \(B = \{-1, 0, 1, 2, 3\}\), does any relation \(F\) from \(A\) to \(B\) contain exactly four ordered pairs?
Given sets \(A\) and \(B\): \(A = \{1, 2, 3, 4\}\) and \(B = \{-1, 0, 1, 2, 3\}\),
---
**(e) Set Membership and Real Numbers**
Does the set of integers \(y\) where \(0 \leq y \leq](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a92f1f7-c382-4ef4-a002-94aeb59ea137%2Fcd74d619-0261-4d2d-bce4-7a9e64960fdd%2F5st0kss_processed.png&w=3840&q=75)
Transcribed Image Text:### Set Theory and Relations: True or False Questions
**Instructions:**
Answer TRUE or FALSE for each of the following statements (a)-(e). Justifications are not required for this problem.
---
**(a) Subsets**
Is the set \(\{3\}\) a subset of the set \(\{-1, 1, 3, 5, 6, 9\}\)?
\[\{3\} \subseteq \{-1, 1, 3, 5, 6, 9\}.\]
---
**(b) Interval Notation and Set Membership**
Does the set \(\{-3, -2, -1, 0, 1, 2\}\) equal the set of real numbers \(x\) that satisfy \(-3 \leq x \leq 2\)?
\[\{-3, -2, -1, 0, 1, 2\} = \{x \in \mathbb{R} \mid -3 \leq x \leq 2\}.\]
---
**(c) Set Inclusion and Square Roots**
Is the set containing \(6\), the set containing \(6\), and the square root of \(6\) squared a subset of the set containing \(6\), the set containing \(6\), and the set whose only element is the set containing \(6\)?
\[\{6, \{6\}, \left(\sqrt{6}\right)^2\} \subseteq \{6, \{6\}, \{\{6\}\}\}.\]
---
**(d) Relations Between Sets**
If \(A = \{1, 2, 3, 4\}\) and \(B = \{-1, 0, 1, 2, 3\}\), does any relation \(F\) from \(A\) to \(B\) contain exactly four ordered pairs?
Given sets \(A\) and \(B\): \(A = \{1, 2, 3, 4\}\) and \(B = \{-1, 0, 1, 2, 3\}\),
---
**(e) Set Membership and Real Numbers**
Does the set of integers \(y\) where \(0 \leq y \leq
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