Inverse Relation R⁻¹ | Relation Defined by y = x − 3
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) \( \{(10,13),(8,11),(12,10)\} \)
(d) none of these
Solution
Given, \[ y=x-3 \]
For \( x=11 \), \[ y=8 \Rightarrow (11,8) \]
For \( x=13 \), \[ y=10 \Rightarrow (13,10) \]
Thus, \[ R=\{(11,8),(13,10)\} \]
Interchanging coordinates, \[ R^{-1}=\{(8,11),(10,13)\} \]
Hence, the correct answer is (a).