Translate the following inference to logic notation: For all x, y is curious if and only if y is happy. For all x, if y were curious, then y is happy. For all x, if y were happy, then y is curious. Therefore for all x, y is curious if and only if y is happy.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).