Translate the following inference to logic notation: If David were a server, then David is drinking water. If David drinks water, then David is a server. For all x, if z were a server, then z is drinking water. Therefore David is a server if and only if David is drinking water.
P(a) -> Q(a). Q(a) -> P(a). forall x: P(x) -> Q(x). Therefore P(a) <-> Q(a).