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
$$
R \cap S
$$
