Find the Inverse Relation \(R^{-1}\)
Question
Find the inverse relation \[ R^{-1} \] if \(R\) is a relation from \[ \{11,12,13\} \] to \[ \{8,10,12\} \] defined by \[ y=x-3. \]
Solution
Using \[ y=x-3 \]
For \[ x=11,\quad y=8 \]
For \[ x=12,\quad y=9 \] but \[ 9\notin\{8,10,12\} \]
For \[ x=13,\quad y=10 \]
Thus,
\[ R=\{(11,8),(13,10)\} \]
Interchanging the coordinates,
\[ R^{-1}=\{(8,11),(10,13)\} \]
Therefore,
\[ \boxed{ R^{-1}=\{(8,11),(10,13)\} } \]