Answer to Question #280282 in Discrete Mathematics for Ashwini

Question

Find matrix and digraph of the relation R=\ (x,y)/xRy iff 2+y is every defined on the set A=\ 1,2,3,4\

Answer 1

Assume $R=\{ (x,y) \forall xRy\}$iff x+y is every defined on the set $A=\{1,2,3,4\}$

Solution:

$R=\{ (x,y) \forall xRy\}$, $A=\{1,2,3,4\}$

So, $R=\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}$

Define

$M_{ij}=0; if\ (x,y)\in R \\ \ \ \ \ \ \ \ \ \ \ \ \ 1; if\ (x,y) \notin R$

So, matrix M =

Digraph: