Translate the following inference to logic notation: For all x, x_8 is a carpenter if and only if x_8 is happy. For all x, if x_8 were a writer, then x_8 is a carpenter. For all x, if x_8 were happy, then x_8 is a writer. Therefore if James were a carpenter, then James is happy.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore P(a) -> Q(a).