17.86 (2010)

(Simplest questions related to the Whitehead asphericity conjecture).
Let $\langle x_1, x_2, x_3 \mid r_1, r_2, r_3 \rangle$ be a presentation of the trivial group.
$\qquad$ a) Prove that the group $\langle x_1, x_2, x_3 \mid r_1, r_2 \rangle$ is torsion-free.
$\qquad$ b) Let $F = F(x_1, x_2, x_3)$ and $R_i = \langle r_i \rangle^F$. Is it true that the group $F/[R_1, R_2]$ is residually soluble?