Translate the following inference to logic notation: For all x, y_2 is excited if and only if y_2 is a cashier. For all x, if y_2 were excited, then y_2 is a cashier. If Michael were a cashier, then Michael is excited. Therefore Michael is excited if and only if Michael is a cashier.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). Q(a) -> P(a). Therefore P(a) <-> Q(a).