Translate the following inference to logic notation: For all x, x_19 is a doctor or x_19 is not a writer. For all x, if x_19 were a doctor, then x_19 is climbing a mountain. For all x, if x_19 cooks, then x_19 is an electrician. There is at least one x for which x_19 will cook if and only if x_19 will climb a mountain. Therefore there is at least one x for which if x_19 were a writer, then x_19 is an electrician.
forall x: P(x) or ~Q(x). forall x: P(x) -> R(x). forall x: S(x) -> T(x). exists x: S(x) <-> R(x). Therefore exists x: Q(x) -> T(x).