Inverse Relation Defined by \( y=x-3 \)
📺 Video Explanation
📝 Question
A relation \( R \) is defined from:
\[ A=\{11,12,13\}, \quad B=\{8,10,12\} \]
by:
\[ y=x-3 \]
Find the inverse relation \(R^{-1}\).
- (a) \(\{(8,11),(10,13)\}\)
- (b) \(\{(11,8),(13,10)\}\)
- (c) \(\{(10,13),(8,11),(8,10)\}\)
- (d) none of these
✅ Solution
🔹 Step 1: Find relation \(R\)
Relation from \(A\) to \(B\) means:
\[ R=\{(x,y): y=x-3\} \]
🔹 Check each element of A
- For \(x=11\): \[ y=11-3=8 \] So: \[ (11,8) \]
- For \(x=12\): \[ y=9 \] But \(9\notin B\), so reject.
- For \(x=13\): \[ y=10 \] So: \[ (13,10) \]
🔹 Relation \(R\)
\[ R=\{(11,8),(13,10)\} \]
🔹 Inverse Relation
Inverse relation is obtained by reversing each ordered pair:
\[ R^{-1}=\{(8,11),(10,13)\} \]
🎯 Final Answer
\[ \boxed{R^{-1}=\{(8,11),(10,13)\}} \]
✔ Correct option: (a)
🚀 Exam Shortcut
- First find valid ordered pairs
- Inverse means swap coordinates
- Only keep values belonging to given sets