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

Range means the set of permissible values of y

Now x and y should lie in a set of natural numbers because the relation is on N

x + 2y = 8

⇒ 2y = 8 – x

⇒ y = 1/2(8 – x) …(i)

Now if we put x > 8 y will be negative which is not in set N (that is not a natural number)

For y to be a natural number (8 – x) has to be an even number

As 8 – x is even, and x has to be less than or equal to 8 hence x can be 8, 6, 4, 2 and 0

Now when we put these values of x in (i), we will get corresponding y values

Hence y = 0, 1, 2, 3 and 4 respectively

Hence range is {0, 1, 2, 3, 4}