Translate the following inference to logic notation: Patricia is a bartender if and only if David is making tea. If David makes tea, then Patricia is a carpenter. For all x, if x_17 were a carpenter, then x_17 is a bartender. Therefore if Patricia were a bartender, then Patricia is a carpenter.
P(a) <-> p. p -> Q(a). forall x: Q(x) -> P(x). Therefore P(a) -> Q(a).