6th EditionTony Gaddis1,223 explanations

6th EditionTony Gaddis1,224 explanations

10th EditionY. Daniel Liang1,626 explanations

5th EditionDavid A. Patterson, John L. Hennessy220 explanations

DISCRETE MATHRefer 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,
$$
R \cup S = \{ ( x , y ) \in A \times B | ( x , y ) \in R
$$
or
$$
( x , y ) \in S \}
$$
,
$$
R \cap S = \{ ( x , y ) \in A \times B | ( x , y ) \in R
$$
and
$$
( x , y ) \in S \}
$$
. Let A={−1, 1, 2, 4} and B={1, 2} 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
$$
x S y \Leftrightarrow x - y
$$
is even. State explicitly which ordered pairs are in
$$
A \times B , R , S, R \cup S
$$
, and
$$
R \cap S
$$