Let R = (x, y) : x, y ϵ Z and x2 + y2 = 25}.


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 $\mathrm{R}=\mathrm{R}^{-1}$.




Put $x=0, y=5,0^{2}+5^{2}=25$

Put $x=3, y=4,3^{2}+4^{2}=25$


Since, $x$ and $y$ get interchanged in the ordered pairs, $R$ and $R^{-1}$

are same.


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