Question:
Let $R$ be a relation on $Z$, defined by $(x, y) \in R \leftrightarrow x^{2}+y^{2}=9$. Then, write $R$ as a set of ordered pairs. What is its domain?
Solution:
$x^{2}+y^{2}=9$
We can have only integral values of x and y.
Put $x=0, y=3,0^{2}+3^{2}=9$
Put $x=3, y=0,3^{2}+0^{2}=9$
$R=\{(0,3),(3,0),(0,-3),(-3,0)\}$
The domain of R is the set of first co-ordinates of R
$\operatorname{Dom}(R)=\{-3,0,3\}$
The range of R is the set of second co-ordinates of R
Range $(R)=\{-3,0,3\}$
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