Let R_1 and R_2 be two relations defined as follows: R_1={( a, b ) ∈ R^2: a^2+ b^2 ∈ Q } and R_2={(a, b) ∈ R^2: a^2+b^2 ∉ Q}, where Q is the set of…

Let $\displaystyle \mathrm{R}_1$ and $\displaystyle \mathrm{R}_2$ be two relations defined as follows : $\displaystyle \mathrm{R}_1=\left\{(\mathrm{a}, \mathrm{b}) \in \mathbf{R}^2: \mathrm{a}^2+\mathrm{b}^2 \in \mathrm{Q}\right\}$ and $\displaystyle R_2=\left\{(a, b) \in \mathbf{R}^2: a^2+b^2 \notin Q\right\}$, where $\displaystyle Q$ is the set of all rational numbers. Then :