Translate the following inference to logic notation: For all x, x_7 will climb a mountain if and only if x_7 is sad. For all x, if x_7 works, then x_7 is sad. For all x, x_7 is a lawyer or x_7 will climb a mountain. There is at least one x for which x_7 is not a lawyer or x_7 will work. Therefore there is at least one x for which x_7 is sad.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: S(x) or P(x). exists x: ~S(x) or R(x). Therefore exists x: Q(x).