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