Translate the following inference to logic notation: It is cold. For all x, if x_2 plays tennis, then x_2 is fast. If Mary reads a book, then it is not cold. David is fast if and only if Mary is reading a book. Therefore David is not playing tennis.
p. forall x: P(x) -> Q(x). q -> ~p. Q(a) <-> q. Therefore ~P(a).