Relation on a Set | Find R if xRy ⇔ y = 3x
Question
If \( R \) is a relation on the set \( A = \{1,2,3,4,5,6,7,8,9\} \) given by \( xRy \iff y=3x \), then \( R = \)
(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
Given, \[ y=3x \]
For \( x=1 \), \[ y=3 \Rightarrow (1,3) \]
For \( x=2 \), \[ y=6 \Rightarrow (2,6) \]
For \( x=3 \), \[ y=9 \Rightarrow (3,9) \]
Thus, \[ R=\{(1,3),(2,6),(3,9)\} \]
Hence, the correct answer is (d) none of these.