Translate the following inference to logic notation: For all x, x_17 will write a letter if and only if x_17 will climb a mountain. There is at least one x for which x_17 will not climb a mountain. For all x, x_17 will write a letter or x_17 is rich. Therefore there is at least one x for which x_17 is rich or x_17 will cook.
forall x: P(x) <-> Q(x). exists x: ~Q(x). forall x: P(x) or R(x). Therefore exists x: R(x) or S(x).