Question:
Let $R=(x, y): x, y \in Z$ and $\left.x^{2}+y^{2}=25\right\}$
Express $\mathrm{R}$ and $\mathrm{R}^{-1}$ as sets of ordered pairs. Show that $\mathrm{R}=\mathrm{R}^{-1}$.
Solution:
$x^{2}+y^{2}=25$
Put $x=0, y=5,0^{2}+5^{2}=25$
Put $x=3, y=4,3^{2}+4^{2}=25$
$R=\{(0,5),(0,-5),(5,0),(-5,0),(3,4),(-3,4),(-3,-4),(3,-4)\}$
Since, $x$ and $y$ get interchanged in the ordered pairs, $R$ and $R^{-1}$
are same.