Question

If A={2,3,4,5,6,7,8,9} let R be a relation on A defined by{(x,y): y belonds to A and x divides y} draw arrow diagram and find R in roster form and domain of R and range of R

Answer 1

Answer:

Roster form of R = { (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (1,7) , (1,8) , (1,9) , (2,2) , (2,4) , (2,6) , (2,8) , (3,3) , (3,6) , (3,9) , (4,4) , (4,8) , (5,5) , (6,6) , (7,7) , (8,8) , (9,9) }

Domain of R = { 1 , 2 , 3 , 4 , 5 ,6 , 7 , 8 , 9 }

Range of R = { 2, 3, 4, 5, 6, 7, 8, 9 }    

Step-by-step explanation:

Given: Set A = { 2, 3, 4, 5, 6, 7, 8, 9 }    

          Relation R = { ( x, y ) : y belongs to A and x divides y}

To find: Arrow Diagram, Roster form , Domain and Range of R.

   

Let x belong to natural no.

then, Roster form of R

R = { (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (1,7) , (1,8) , (1,9) , (2,2) , (2,4) , (2,6) , (2,8) ,

         (3,3) , (3,6) , (3,9) , (4,4) , (4,8) , (5,5) , (6,6) , (7,7) , (8,8) , (9,9) }

Domain of R:

Let say Set B is domain of R, then B = { 1 , 2 , 3 , 4 , 5 ,6 , 7 , 8 , 9 }

or B = { x : x ∈ N and x ≤ 9}

Range of R:

Let say set C defines Range of R, then C = { 2 , 3 , 4 ,5 , 6 , 7 , 8 , 9 }

Range of R = Set A

Arrow Diagram is Attached.

Answer 2

Answer:

{(x,y):x and y belongs to A and x divides y}

1. R = {(2,2),(2,4),(2,6),(2,8),(3,3),(3,6),(3,9),(4,4),(4,8),((5,5),(6,6),(7,7),(8,8),(9,9)}

2. Domain of R = {2,3,4,5,6,7,8,9}

3. Range of R = {2,3,4,5,6,7,8,9}.