Test validity by the tree method. (a) Alma paints, so someone does: Pa, so 3x Px. (b) Someone paints, so Alma does. (c) Alma loves someone, for she loves the Baron. (d) Of course Alma loves herself—everyone does: Vx Lxx, so Laa. (e) Someone sings, so someone paints, for all singers paint: 3x Sx, Vx (Sx → Px), so 3x Px.