Domain of a Relation on Integers | x² + y² ≤ 4
Question
If \[ R=\{(x,y):x,y\in Z,\ x^2+y^2\le4\} \] is a relation on \( Z \), then domain of \( R \) is
(a) \( \{0,1,2\} \)
(b) \( \{0,-1,-2\} \)
(c) \( \{-2,-1,0,1,2\} \)
(d) none of these
Solution
Given, \[ x^2+y^2\le4 \]
Since \( y^2\ge0 \), \[ x^2\le4 \]
Therefore, \[ -2\le x\le2 \]
Hence, \[ \text{Domain of }R=\{-2,-1,0,1,2\} \]
Therefore, the correct answer is (c).