Translate the following inference to logic notation: For all x, x_7 is an astronaut. For all x, if x_7 were an astronaut, then x_7 is climbing a mountain. There is at least one x for which x_7 is a scientist or x_7 will not climb a mountain. Therefore there is at least one x for which x_7 is a scientist.
forall x: P(x). forall x: P(x) -> Q(x). exists x: R(x) or ~Q(x). Therefore exists x: R(x).