Write the Relation as a Set of Ordered Pairs
Question
Write the following relation as the set of ordered pairs:
A relation \(R\) on the set \[ \{0,1,2,\ldots,10\} \] defined by \[ 2x+3y=12. \]
Solution
Given,
\[ 2x+3y=12 \]
For \[ x=0,\quad y=4 \]
\[ (0,4) \]
For \[ x=3,\quad y=2 \]
\[ (3,2) \]
For \[ x=6,\quad y=0 \]
\[ (6,0) \]
Therefore,
\[ \boxed{ R=\{(0,4),(3,2),(6,0)\} } \]