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, RUS = {(x, y) E Ax BI (X, y) ER or (x, y) E S} RNS = {(x, y) E Ax BI (x, y) € R and (x, y) E S}. Let A = {-4, 4, 7, 9} and B = (4, 7}, and define relations R and S from A to B as follows. For every (x, y) E Ax B, x R y |x| = lyl and x Syex - y is even. Which ordered pairs are in A x B, R, S, RU S, and RN S? (Use set-roster notation to enter your answers.) AxB = R =
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, RUS = {(x, y) E Ax BI (X, y) ER or (x, y) E S} RNS = {(x, y) E Ax BI (x, y) € R and (x, y) E S}. Let A = {-4, 4, 7, 9} and B = (4, 7}, and define relations R and S from A to B as follows. For every (x, y) E Ax B, x R y |x| = lyl and x Syex - y is even. Which ordered pairs are in A x B, R, S, RU S, and RN S? (Use set-roster notation to enter your answers.) AxB = R =
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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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 \( A = \{-4, 4, 7, 9\} \) and \( B = \{4, 7\} \), 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 \( x S y \Leftrightarrow x - y \) is even.
Which ordered pairs are in \( A \times B \), \( R \), \( S \), \( R \cup S \), and \( R \cap S \)? (Use set-roster notation to enter your answers.)
\( A \times B = \)
\[ \qquad \]
\( R = \)
\[ \qquad \]
\( S = \)
\[ \qquad \]
\( R \cup S = \)
\[ \qquad \]
\( R \cap S = \)
\[ \qquad \]
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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 \( A = \{-4, 4, 7, 9\} \) and \( B = \{4, 7\} \), 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 \( x S y \Leftrightarrow x - y \) is even.
Which ordered pairs are in \( A \times B \), \( R \), \( S \), \( R \cup S \), and \( R \cap S \)? (Use set-roster notation to enter your answers.)
\( A \times B = \)
\[ \qquad \]
\( R = \)
\[ \qquad \]
\( S = \)
\[ \qquad \]
\( R \cup S = \)
\[ \qquad \]
\( R \cap S = \)
\[ \qquad \]
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