Consider the relations R_1 and R_2 defined as a R_1 b ⇔ a^2+b^2=1 for all a, b ∈ R and (a, b) R_2(c, d) ⇔ a + d = b + c for all ( a, b ),( c, d ) ∈ N…

Consider the relations $\displaystyle R_1$ and $\displaystyle R_2$ defined as $\displaystyle a R_1 b \Leftrightarrow a^2+b^2=1$ for all $\displaystyle a, b \in R$ and $\displaystyle (a, b) R_2(c, d) \Leftrightarrow$ $\displaystyle \mathrm{a}+\mathrm{d}=\mathrm{b}+\mathrm{c}$ for all $\displaystyle (\mathrm{a}, \mathrm{b}),(\mathrm{c}, \mathrm{d}) \in \mathrm{N} \times \mathrm{N}$. Then