Translate the following inference to logic notation: There is at least one x for which x_15 is a doctor or x_15 will read a book. For all x, x_15 is not a carpenter. For all x, x_15 will read a book if and only if x_15 is a carpenter. For all x, if x_15 were a doctor, then x_15 is a carpenter. Therefore there is at least one x for which x_15 will play tennis.
exists x: P(x) or Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: P(x) -> R(x). Therefore exists x: S(x).