Inverse Relation R⁻¹ | Find the Inverse of a Relation
Question
Let \( A=\{1,2,3\} \), \( B=\{1,3,5\} \). If relation \[ R=\{(1,3),(2,5),(3,3)\} \] from \( A \) to \( B \), then \( R^{-1} \) is
(a) \( \{(3,1),(3,1),(5,2)\} \)
(b) \( \{(1,3),(2,5),(3,3)\} \)
(c) \( \{(1,3),(5,2)\} \)
(d) none of these
Solution
To find \( R^{-1} \), interchange the coordinates of each ordered pair.
\[ (1,3)\Rightarrow(3,1) \]
\[ (2,5)\Rightarrow(5,2) \]
\[ (3,3)\Rightarrow(3,3) \]
Therefore, \[ R^{-1}=\{(3,1),(5,2),(3,3)\} \]
Hence, the correct answer is (d) none of these.