Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 141 / 1 / b / Solution

The generators are the alpha-compressing disks, equivalently the four bounded regions. Each beta curve supplies the relator read from its signed intersections with the alpha curves. Since the basepoint region has generator $r_0=1$, the presentation isThe relations say $d=ba=cb=ac$. Eliminating $c,d$ leaves $bab=aba$, the standard two-generator presentation of the trefoil knot group, which checks the region conventions.