Translate the following inference to logic notation: If Richard writes a letter, then Mary is not excited. Mary is excited. For all x, x_17 will write a letter if and only if x_17 will play tennis. It is overcast if and only if Richard is playing tennis. Therefore it is not overcast.
P(a) -> ~p. p. forall x: P(x) <-> Q(x). q <-> Q(a). Therefore ~q.