Translate the following inference to logic notation: If it is overcast, then William is a cashier. If Thomas were an office clerk, then William is playing a game. It is overcast or Thomas is an office clerk. For all x, if z plays a game, then z is a cashier. Therefore William is a cashier.
p -> P(a). q -> Q(a). p or q. forall x: Q(x) -> P(x). Therefore P(a).