Question

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R⁻¹ is
(a) {(8, 11), (10, 13)}
(b) {(11, 8), (13, 10)}
(c) {(10, 13), (8, 11)}
(d) none of these

Answer 1

(a) {(8, 11), (10, 13)}

The relation R is defined by
$$\begin{gathered} R=\left\{\left(x,y\right):x\in \left\{11,12,13\right\},y\in \left\{8,10,12\right\}:y=x-3\right\} \\ \Rightarrow R=\left\{\left(11,8\right),(13,10)\right\} \\ \mathrm{So},R^{-1}=\left\{\left(8,11\right),\left(10,13\right)\right\} \end{gathered}$$