Relation on \( A=\{1,2,3,4,5,6,7,8,9\} \) Defined by \( y=3x \)
📺 Video Explanation
📝 Question
Let \[ A=\{1,2,3,4,5,6,7,8,9\} \]
A relation \(R\) on \(A\) is defined by:
\[ xRy \iff y=3x \]
Find \(R\).
- (a) \(\{(3,1),(6,2),(8,2),(9,3)\}\)
- (b) \(\{(3,1),(6,2),(9,3)\}\)
- (c) \(\{(3,1),(2,6),(3,9)\}\)
- (d) none of these
✅ Solution
Relation means all ordered pairs \((x,y)\in A\times A\) such that:
\[ y=3x \]
🔹 Check possible values of \(x\)
- For \(x=1\): \[ y=3 \] Valid pair: \[ (1,3) \]
- For \(x=2\): \[ y=6 \] Valid pair: \[ (2,6) \]
- For \(x=3\): \[ y=9 \] Valid pair: \[ (3,9) \]
- For \(x\geq4\): \[ y>9 \] Not in set.
🔹 Relation Set
\[ R=\{(1,3),(2,6),(3,9)\} \]
🔹 Match with Options
None of the given options exactly match this set.
Option (c) contains reversed first pair:
\[ (3,1) \] instead of:
\[ (1,3) \]
So incorrect.
🎯 Final Answer
\[ \boxed{\text{none of these}} \]
✔ Correct option: (d)
🚀 Exam Shortcut
- Use relation rule directly: \(y=3x\)
- Keep only pairs inside set
- Check order carefully in MCQs