Find the Domain of Relation R Where x² + y² = 9
Question
If \( R \) is a relation defined on the set \( Z \) of integers by the rule
\[ (x,y)\in R \iff x^2+y^2=9, \]
then write domain of \( R \).
Solution
Given,
\[ x^2+y^2=9 \]
Possible integer pairs are:
\[ (0,3),(0,-3),(3,0),(-3,0) \]
Therefore, the domain is the set of first components.
\[ \text{Domain}(R)=\{-3,0,3\} \]
Hence,
\[ \boxed{\{-3,0,3\}} \]