Let A = {4, 5, 6} and B {6, 7, 8} and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E A × B, XS y = x\y. Using set-roster notation, state explicitly which ordered pairs are in S and S¯4. (Enter your answers as comma-separated lists of ordered pairs.) S = s-1
Let A = {4, 5, 6} and B {6, 7, 8} and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E A × B, XS y = x\y. Using set-roster notation, state explicitly which ordered pairs are in S and S¯4. (Enter your answers as comma-separated lists of ordered pairs.) S = s-1
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Author:Erwin Kreyszig
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![### Educational Exercise on Set Theory and Relations
**Exercise: Understanding the "Divides" Relation**
Let \( A = \{4, 5, 6\} \) and \( B = \{6, 7, 8\} \), and let \( S \) be the "divides" relation from \( A \) to \( B \). That is, for every ordered pair \( (x, y) \in A \times B \),
\[ x \mathrel{S} y \iff x \mid y. \]
**Task:**
Using set-roster notation, state explicitly which ordered pairs are in \( S \) and \( S^{-1} \).
**Instructions:**
- Enter your answers as comma-separated lists of ordered pairs.
**Set \( S \):**
\[ S = \boxed{} \]
**Inverse Set \( S^{-1} \):**
\[ S^{-1} = \boxed{} \]
**Explanation of the Concept:**
- **Divides Relation (\(x \mid y\)):** This means \( x \) is a divisor of \( y \). For example, \( 4 \mid 8 \) because \( 8 / 4 = 2 \), which is an integer.
- **Ordered Pair (\(x, y\)):** A pair where the order matters, denoted as \( (x, y) \).
- **Set-Roster Notation:** A way of representing sets by listing their elements, enclosed in curly brackets. For example, the set of natural numbers less than 5 can be written as \( \{1, 2, 3, 4\} \).
**Formulating the Solutions:**
1. **Identify the Ordered Pairs in Set \( S \):**
- \( (4, 6) \): \( 4 \) does not divide \( 6 \) (since \( 6/4 \) is not an integer)
- \( (4, 7) \): \( 4 \) does not divide \( 7 \)
- \( (4, 8) \): \( 4 \) divides \( 8 \)
- \( (5, 6) \): \( 5 \) does not divide \( 6 \)
- \( (5, 7) \): \( 5 \) does not divide \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F507ffaff-36d6-4c89-a9b8-d054ae79319d%2F1574abf7-b86c-4ce0-842b-9e4a22711bc7%2Fusfii4a.png&w=3840&q=75)
Transcribed Image Text:### Educational Exercise on Set Theory and Relations
**Exercise: Understanding the "Divides" Relation**
Let \( A = \{4, 5, 6\} \) and \( B = \{6, 7, 8\} \), and let \( S \) be the "divides" relation from \( A \) to \( B \). That is, for every ordered pair \( (x, y) \in A \times B \),
\[ x \mathrel{S} y \iff x \mid y. \]
**Task:**
Using set-roster notation, state explicitly which ordered pairs are in \( S \) and \( S^{-1} \).
**Instructions:**
- Enter your answers as comma-separated lists of ordered pairs.
**Set \( S \):**
\[ S = \boxed{} \]
**Inverse Set \( S^{-1} \):**
\[ S^{-1} = \boxed{} \]
**Explanation of the Concept:**
- **Divides Relation (\(x \mid y\)):** This means \( x \) is a divisor of \( y \). For example, \( 4 \mid 8 \) because \( 8 / 4 = 2 \), which is an integer.
- **Ordered Pair (\(x, y\)):** A pair where the order matters, denoted as \( (x, y) \).
- **Set-Roster Notation:** A way of representing sets by listing their elements, enclosed in curly brackets. For example, the set of natural numbers less than 5 can be written as \( \{1, 2, 3, 4\} \).
**Formulating the Solutions:**
1. **Identify the Ordered Pairs in Set \( S \):**
- \( (4, 6) \): \( 4 \) does not divide \( 6 \) (since \( 6/4 \) is not an integer)
- \( (4, 7) \): \( 4 \) does not divide \( 7 \)
- \( (4, 8) \): \( 4 \) divides \( 8 \)
- \( (5, 6) \): \( 5 \) does not divide \( 6 \)
- \( (5, 7) \): \( 5 \) does not divide \(
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