Answer to Question #243316 in Discrete Mathematics for MUHAMMAD ABID

Question

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) EA x B. XRyoxly for all (x,y) EA x B x Syy-4 = x State explicitly which ordered pairs are in A x B. R, S, RUS and Ros. And draw the Coordinate Graph, Arrow Diagram & Directed Graph for each.

Answer 1

$A=\{2,4\}~~~B=\{6,8,10\}$

$xRy$ if $x|y$

$R=\{(2,6),(2,8),(2,10),(4,8)\}$

$xSy$ if $y-4=x$

$S=\{(2,6),(4,8)\}$

$A\times B=\{(2,6),(2,8),(2,10),(4,6),(4,8),(4,10)\}\\ R\cup S=\{(2,6),(2,8),(2,10),(4,8)\}\\ RoS=\phi$

The coordinate graph for the relation is as follows;

The arrow diagram for the relations is as follows;

The directed graph for the relations is as follows;