Translate the following inference to logic notation: For all x, x_11 is excited if and only if x_11 will climb a mountain. For all x, x_11 is excited if and only if x_11 will climb a mountain. Therefore if Sarah were excited, then Sarah is climbing a mountain.
forall x: P(x) <-> Q(x). forall x: P(x) <-> Q(x). Therefore P(a) -> Q(a).