Let A = {-4, 4, 5, 9} and B = {4, 5} and define relations R and S from A to B as follows: For every (x, y) E A x B, x Ry + |x| = \y[ and %3D x S y x - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, R U S, and R n S. (Enter your answers as comma-separated lists of ordered pairs.) АхВ %3 R = = S RUS = Rn S =
Let A = {-4, 4, 5, 9} and B = {4, 5} and define relations R and S from A to B as follows: For every (x, y) E A x B, x Ry + |x| = \y[ and %3D x S y x - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, R U S, and R n S. (Enter your answers as comma-separated lists of ordered pairs.) АхВ %3 R = = S RUS = Rn S =
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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![**Unions and Intersections of Relations**
This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations \( R \) and \( S \) from a set \( A \) to a set \( B \),
\[ R \cup S = \{(x, y) \in A \times B \mid (x, y) \in R \text{ or } (x, y) \in S\} \]
\[ R \cap S = \{(x, y) \in A \times B \mid (x, y) \in R \text{ and } (x, y) \in S\} \]
Let \( A = \{-4, 4, 5, 9\} \) and \( B = \{4, 5\} \) and define relations \( R \) and \( S \) from \( A \) to \( B \) as follows: For every \( (x, y) \in A \times B \),
\[ x \, R \, y \iff |x| = |y| \text{ and} \]
\[ x \, S \, y \iff x - y \text{ is even}\]
Using set-roster notation, state explicitly which ordered pairs are in \( A \times B \), \( R \), \( S \), \( R \cup S \), and \( R \cap S \). (Enter your answers as comma-separated lists of ordered pairs.)
\[ A \times B = \text{[ ]} \]
\[ R = \text{[ ]} \]
\[ S = \text{[ ]} \]
\[ R \cup S = \text{[ ]} \]
\[ R \cap S = \text{[ ]} \]
**Diagram Explanation:**
The diagram includes a series of lines of mathematical text defining concepts related to set theory and relations, along with boxes for entering specific sets of ordered pairs. The text explains how to calculate union and intersection for relations \( R \) and \( S \) given specific sets \( A \) and \( B \). Additionally, it provides a specific example and asks students to apply the theoretical explanation to determine various sets \( A \times B \), \( R \), \( S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F507ffaff-36d6-4c89-a9b8-d054ae79319d%2F6b585489-b648-479d-bdf0-fef189680c43%2F3qls9zu.png&w=3840&q=75)
Transcribed Image Text:**Unions and Intersections of Relations**
This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations \( R \) and \( S \) from a set \( A \) to a set \( B \),
\[ R \cup S = \{(x, y) \in A \times B \mid (x, y) \in R \text{ or } (x, y) \in S\} \]
\[ R \cap S = \{(x, y) \in A \times B \mid (x, y) \in R \text{ and } (x, y) \in S\} \]
Let \( A = \{-4, 4, 5, 9\} \) and \( B = \{4, 5\} \) and define relations \( R \) and \( S \) from \( A \) to \( B \) as follows: For every \( (x, y) \in A \times B \),
\[ x \, R \, y \iff |x| = |y| \text{ and} \]
\[ x \, S \, y \iff x - y \text{ is even}\]
Using set-roster notation, state explicitly which ordered pairs are in \( A \times B \), \( R \), \( S \), \( R \cup S \), and \( R \cap S \). (Enter your answers as comma-separated lists of ordered pairs.)
\[ A \times B = \text{[ ]} \]
\[ R = \text{[ ]} \]
\[ S = \text{[ ]} \]
\[ R \cup S = \text{[ ]} \]
\[ R \cap S = \text{[ ]} \]
**Diagram Explanation:**
The diagram includes a series of lines of mathematical text defining concepts related to set theory and relations, along with boxes for entering specific sets of ordered pairs. The text explains how to calculate union and intersection for relations \( R \) and \( S \) given specific sets \( A \) and \( B \). Additionally, it provides a specific example and asks students to apply the theoretical explanation to determine various sets \( A \times B \), \( R \), \( S
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