Question

Let A be the set of first ten natural numbers and let R be a relation in A defined by (x, y) $ϵ$ R is and only if x + 2y = 10. Which of the following is false?

• A. R = {(2, 4), (4, 3), (6, 2),(8, 1)}
• B. Domain of R = {2, 4, 6, 8}
• C. Range of R = {1, 2, 3, 4}
• D. At least one is false

Answer 1

The correct option is D At least one is false

We have,
R = {(x, y): x, y $ϵ$ N, x + 2y = 10, 1 $\le$ x, y $\le$ 10}
X + 2y = 10 $\Rightarrow$ y = $\frac{10-x}{2}$
$\therefore$ R = {(2,4), (4,3), (6,2), (8,1)}
Domain of R {x: (x, y) $ϵ$ R } = {2, 4, 6, 8}
Range of R = {y: (x, y) $ϵ$R} = {4, 3, 2, 1}