Translate the following inference to logic notation: For all x, x_13 is sad if and only if x_13 will climb a mountain. For all x, x_13 is a writer. There is at least one x for which x_13 will climb a mountain. Therefore there is at least one x for which x_13 is sad and x_13 is a writer.
forall x: P(x) <-> Q(x). forall x: R(x). exists x: Q(x). Therefore exists x: P(x) and R(x).