# Let R be a relation on N defined by x + 2y = 8. The domain of R is

Question:

Let R be a relation on N defined by + 2y = 8. The domain of R is

(a) {2, 4, 8}
(b) {2, 4, 6, 8}
(c) {2, 4, 6}
(d) {1, 2, 3, 4}

Solution:

(c) {2,4,6}

The relation R is defined as

$R=\{(x, y): x, y \in N$ and $x+2 y=8\}$

$\Rightarrow R=\left\{(x, y): x, y \in N\right.$ and $\left.y=\frac{(8-x)}{2}\right\}$

Domain of $R$ is all values of $x \in N$ satisfying the relation $R$. Also, there are only three values of $x$ that result in $y$, which is a natural number. These are $\{2,6,4\}$.