This question refers to unions and intersections of relations. Since relations are subsets a 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, RUS= {(x, y) EAxBI (x, y) ER or (x, y) ES} Rns= ((x, y) EAXB|(x, y) ER and (x, y) ES). Let A = (-2, 2, 5, 7) and B=(2, 5) and define relations R and S from A to B as follows: For every (x, y) EA x B, x Ry |x| = lyl and xSysx-y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RUS, and Rn S. (Enter your answers as comma-separated lists of ordered pairs.) Ax B = R = S = RUS = Rns=
This question refers to unions and intersections of relations. Since relations are subsets a 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, RUS= {(x, y) EAxBI (x, y) ER or (x, y) ES} Rns= ((x, y) EAXB|(x, y) ER and (x, y) ES). Let A = (-2, 2, 5, 7) and B=(2, 5) and define relations R and S from A to B as follows: For every (x, y) EA x B, x Ry |x| = lyl and xSysx-y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RUS, and Rn S. (Enter your answers as comma-separated lists of ordered pairs.) Ax B = R = S = RUS = Rns=
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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![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 \( A = \{-2, 2, 5, 7\} \) and \( B = \{2, 5\} \) and define relations \( R \) and \( S \) from \( A \) to \( B \) as follows: For every \((x, y) \in A \times B\),
- \( x \, R \, y \Leftrightarrow |x| = |y| \) and
- \( x \, S \, y \Leftrightarrow x - y \text{ is even} \).
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.)
- \( A \times B = \)
- \( R = \)
- \( S = \)
- \( R \cup S = \)
- \( R \cap S = \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F9d2f8641-ff06-428b-9f1d-2423a3a742af%2Fa7iop2_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 \( A = \{-2, 2, 5, 7\} \) and \( B = \{2, 5\} \) and define relations \( R \) and \( S \) from \( A \) to \( B \) as follows: For every \((x, y) \in A \times B\),
- \( x \, R \, y \Leftrightarrow |x| = |y| \) and
- \( x \, S \, y \Leftrightarrow x - y \text{ is even} \).
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.)
- \( A \times B = \)
- \( R = \)
- \( S = \)
- \( R \cup S = \)
- \( R \cap S = \)
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