Translate the following inference to logic notation: Mary is climbing a mountain if and only if Mary is an astronaut. For all x, if x_10 were an astronaut, then x_10 is climbing a mountain. Therefore Mary is climbing a mountain if and only if Mary is an astronaut.
P(a) <-> Q(a). forall x: Q(x) -> P(x). Therefore P(a) <-> Q(a).