Translate the following inference to logic notation: There is at least one x for which z_2 will climb a mountain if and only if z_2 is a cashier. For all x, z_2 is a cashier or z_2 will not climb a mountain. Therefore there is at least one x for which z_2 is a cashier if and only if z_2 will climb a mountain.
exists x: P(x) <-> Q(x). forall x: Q(x) or ~P(x). Therefore exists x: Q(x) <-> P(x).