Question

Let A = {1,2,3,4,5,6) and R be the relation defined on A by R= {(x, y): x,y e A,x divides y), then range of R is ​

Answer 1

Step-by-step explanation:

Given :-

Let A = {1,2,3,4,5,6) and R be the relation defined on A by R= {(x, y): x,y € A, x divides y)}

To find :-

Find the range of R ?

Solution :-

Given set is A = { 1,2,3,4,5,6}

Given relation = R

R is defined by {(x, y): x,y € A,x divides y)}

1 divides 1 then the order pair = (1,1)

1 divides 2 then the order pair = (1,2)

1 divides 3 then the order pair = (1,3)

1 divides 4 then the order pair = (1,4)

1 divides 5 then the order pair = (1,5)

1 divides 6 then the order pair = (1,6)

2 divides 4 then the order pair = (2,4)

2 divides 6 then the order pair = (2,6)

3 divides 6 then the order pair = (3,6)

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

The set of first elements in the order pair of R

= { 1,2,3)

Domain of R = {1,2,3}

The set of second elements in the order pair of R

= { 1,2,3,4,5,6}

Range of R = { 1,2,3,4,5,6}

Answer:-

The range of R for the given problem is {1,2,3,4,5,6}

Used formulae:-

• The set of first elements in an ordered pair is called the Domain .
• The set of second elements in an ordered pair is called the Range .
• 1 divides every number .
• 1 is the factor of every number.