Find the Inverse Relation \(R^{-1}\)
Question
Find the inverse relation \[ R^{-1} \] if
\[ R=\{(x,y):x,y\in N,\ x+2=8\} \]
Solution
Given,
\[ x+2=8 \]
\[ x=6 \]
Thus,
\[ R=\{(6,y):y\in N\} \]
Interchanging the coordinates,
\[ R^{-1}=\{(y,6):y\in N\} \]
Therefore,
\[ \boxed{ R^{-1}=\{(y,6):y\in N\} } \]