Translate the following inference to logic notation: If Charles were happy, then Charles is drinking water. For all x, if x_12 drinks water, then x_12 is happy. If Charles were happy, then Charles is drinking water. Therefore Charles is happy if and only if Charles is drinking water.
P(a) -> Q(a). forall x: Q(x) -> P(x). P(a) -> Q(a). Therefore P(a) <-> Q(a).