Find the Inverse Relation \(R^{-1}\)
Question
Find the inverse relation \[ R^{-1} \] if
\[ R= \{ (1,2),(1,3),(2,3),(3,2),(5,6) \} \]
Solution
To find \[ R^{-1}, \] interchange the coordinates of each ordered pair.
\[ (1,2)\rightarrow(2,1) \]
\[ (1,3)\rightarrow(3,1) \]
\[ (2,3)\rightarrow(3,2) \]
\[ (3,2)\rightarrow(2,3) \]
\[ (5,6)\rightarrow(6,5) \]
Therefore,
\[ \boxed{ R^{-1} = \{ (2,1),(3,1),(3,2),(2,3),(6,5) \} } \]