Question

If R = {(x, y) : x + 2y = 8} is a relation on N, write the range of R.

Answer 1

Sol.  R = {(x, y) : x + 2y = 8} is a relation on N

              Then we can say 2y = 8 - x

                                         y=4−x2y=4−x2

              so we can put the value of x, x = 2, 4, 6 only
              we get y = 3 at x = 2
              we get y = 2 at x = 4
              we get y = 1 at x = 6
              so range = {1, 2, 3} Ans.

Answer 2

The range of R in a given relation is {1,2,3}

Step-by-step explanation:

Given: The given equation is x+2y =8

x, y are natural numbers, which states that x,y > 0

To find: The range R for a given equation

R = {(x,y): x+2y =8

N = set of natural numbers

x = domain

y = range

From the given equation take y value,

2y = 8 -x

$y = \frac{8 - x}{2}$

$y = 4 - \frac{x}{2}$

Sub x= 2 in the above equation

y = 4 - 1

y=3

Sub x=4

y = 4 - 2

y = 2

Sub x = 6

y = 4 - 3

y = 1

For y>4 ,  x wont be a natural number

so the range is {1 ,2, 3]

Final answer:

The range of R in a given relation is {1,2,3}

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