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