The Relation R = {(x, y) : x, y ∈ Z, x² + y² = 64} is ……………………….
Question
The relation
\[ R = \{(x,y): x,y\in Z,\ x^2+y^2=64\} \]
is ……………………….
Solution
We are given:
\[ x^2+y^2=64 \]
where \( x \) and \( y \) are integers.
Since
\[ 64=8^2 \]
only a limited number of integer pairs can satisfy this equation.
Possible integer solutions are:
\[ (0,8),\ (0,-8),\ (8,0),\ (-8,0) \]
These are only finitely many ordered pairs.
Therefore, the relation contains a finite number of elements.
Hence, the relation \( R \) is:
\[ \boxed{\text{finite}} \]