Translate the following inference to logic notation: For all x, if x_5 were a carpenter, then x_5 is happy. There is at least one x for which x_5 is poor or x_5 is a carpenter. For all x, if x_5 were happy, then x_5 is poor. For all x, if x_5 were poor, then x_5 is happy. Therefore there is at least one x for which x_5 is happy.
forall x: P(x) -> Q(x). exists x: R(x) or P(x). forall x: Q(x) -> R(x). forall x: R(x) -> Q(x). Therefore exists x: Q(x).