Question

Let R be a relation on N defined by x + 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}

Answer 1

(c) {2,4,6}

The relation R is defined as
$$\begin{gathered} R=\left\{\left(x,y\right):x,y\in N\mathrm{and}x+2y=8\right\} \\ \Rightarrow R=\left\{\left(x,y\right):x,y\in N\mathrm{and}y=\frac{\left(8-x\right)}{2}\right\} \end{gathered}$$

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}.