Answer to Question #117154 in Combinatorics | Number Theory for Priya

Question

Consider the relation R={(a,b)|a divides b} on the set {1,2,3,4,5,6}
(a)List all the ordered pairs in R.
(b) Draw the digraph of R

Answer 1

Both sets A and B contain 1,2,3,4,5 6

Ordered pairs in the set R are (a,b)

Where a is element of A

and b is element of B

According to given question an ordered pair is part of R if a divides bý

1) 1 divides all numbers

(1,b) =b/1= b

So (1,b) is part are part of set

2) an integer may be divided itself (a/a)=1

( a,a) =a/a=1

So (a,a) is part of set

AxB={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1)(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,5),(5,6),(6,1),(6,2),(6,3),(6, 4),(6,5),(6,6)}

Relation ={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,2),(2,4),(2,6),

(3,3),(3,6),

(4,4),

(5,5),

(6,6)

}

Diagraph of R

This diagram shows if elements of B divided by A then element of A connected

B

FOR EXAMPLE

1 CONNECTED 1,2,3,4,5,6

1,2,3,4,5,6 divided by 1

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

2) (2,2)(2,4) ( 2,6)

(a,b)b/a

2/2 ,4/2 ,6/2

So 2 CONNECTED 2,4,5,6

3) 3 connect 3,6

4) 4 connected 4

5) 5 connected 5

6) 6 connected 6

Tabular form