Solved: Exercises 1920 refer to unions and intersections of relations. Since relations

Chapter 8, Problem 19

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Exercises 19–20 refer 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 to B,

R \(\cup\) S = {(x, y) \(\in\) A × B | (x, y) \(\in\) R or (x, y) \(\in\) S}

R \(\bigcap\) S = {(x, y) \(\in\) A × B | (x, y) \(\in\) R and (x, y) \(\in\) S}.

Let A = {2, 4} and B = {6, 8, 10} and define relations R and S from A to B as follows: For all (x, y) \(\in\) A \(\times\) B,

x R y \(\Leftrightarrow\) x | y and

x S y \(\Leftrightarrow\) y − 4 = x.

State explicitly which ordered pairs are in A \(\times\) B, R, S, R (\cup\) S, and R \(\bigcap\) S.

Text Transcription:

cup

in

times

bigcap

Leftrightarrow