Translate the following inference to logic notation: If Patricia were excited, then Robert is a sailor. If Robert takes a plane, then Patricia is excited. For all x, x_4 will take a plane if and only if x_4 is a sailor. Therefore Robert is taking a plane if and only if Robert is a sailor.
p -> P(a). Q(a) -> p. forall x: Q(x) <-> P(x). Therefore Q(a) <-> P(a).