Translate the following inference to logic notation: For all x, x_5 is a scientist. For all x, if x_5 were a scientist, then x_5 is a carpenter. For all x, if x_5 were a carpenter, then x_5 is running. Therefore for all x, x_5 will go running or x_5 is sad.
forall x: P(x). forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). Therefore forall x: R(x) or S(x).