Translate the following inference to logic notation: For all x, x_12 is happy if and only if x_12 is a bartender. Michael is playing squash if and only if Elisabeth is a bartender. Elisabeth is not happy. Mary is a cashier if and only if Michael is playing squash. Therefore Mary is not a cashier.
forall x: P(x) <-> Q(x). p <-> Q(a). ~P(a). q <-> p. Therefore ~q.