UPSC NDA Math Model Paper 2

Since R is a relation on ℕ, the elements x and y must be positive integers.
We have x + 2y = 8.
⇒y=

8−x

2

=4−

x

2

For y to be positive and an integer (y ∈ N), we conclude that x must be divisible by 2 and 4−

x

2

>0
⇒4>

x

2

⇒x<8
The only numbers less than 8 which are divisible by 2 are 2, 4 and 6.
∴ x ∈ {2, 4, 6} which is the required range.