Translate the following inference to logic notation: If Patricia takes a plane, then it is windy. For all x, x_19 will take a plane if and only if x_19 will make tea. It is windy if and only if Patricia is making tea. Therefore Patricia is making tea if and only if it is windy.
P(a) -> p. forall x: P(x) <-> Q(x). p <-> Q(a). Therefore Q(a) <-> p.