Translate the following inference to logic notation: There is at least one x for which if z plays tennis, then z is climbing a mountain. For all x, if z were a writer, then z is playing tennis. For all x, z is a writer if and only if z will climb a mountain. Therefore there is at least one x for which z will climb a mountain if and only if z is a writer.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: R(x) <-> Q(x). Therefore exists x: Q(x) <-> R(x).