Let $A = \{ 2,3,4,5,6,7,8 \}$ and define a relation $R$ on $A$ as follows: for all $x , y \in A$,
$x R y \Leftrightarrow 3 \mid ( x - y ) .$
(a) Is $7 R 2$ ? Is $13 R 4$ ? Is $2 R 5$ ? Is $8 R 8$ ?
(b) Draw the directed graph of $R$.

Question

Quizplus · Accepted Answer

The Answer is a.

7 R 2

because

7 - 2 = 5

and

3 mid 5 ; \quad 13 R 4

because

13 - 4 = 9

and

3 \mid 9

;

2 R 5

because

2 - 5 = - 3

and

3 \mid - 3 ; \quad 8 R 8

because

8 - 8 = 0

and

3 \mid 0

.
b. Draw the directed graph of

R

.
$a. 7 R 2 because 7 - 2 = 5 and 3 mid 5 ; \quad 13 R 4 because 13 - 4 = 9 and 3 \mid 9 ; 2 R 5 because 2 - 5 = - 3 and 3 \mid - 3 ; \quad 8 R 8 because 8 - 8 = 0 and 3 \mid 0 . b. Draw the directed graph of R .$

Let A={2,3,4,5,6,7,8}A = \{ 2,3,4,5,6,7,8 \}A={2,3,4,5,6,7,8} And Define a Relation RRR On AAA

Let $A = \{ 2,3,4,5,6,7,8 \}$ And Define a Relation $R$ On $A$