Translate the following inference to logic notation: If John plays tennis, then Joseph is listening to a song. If Patricia were a mechanic, then John is playing a game. For all x, if x_10 plays a game, then x_10 is playing tennis. Therefore if Patricia were a mechanic, then Joseph is listening to a song.
P(a) -> p. q -> Q(a). forall x: Q(x) -> P(x). Therefore q -> p.