Translate the following inference to logic notation: For all x, x_8 will cook. For all x, if x_8 were a doctor, then x_8 is drinking water. For all x, x_8 is a scientist. For all x, if x_8 were a scientist, then x_8 is a doctor. Therefore Patricia is cooking.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x). forall x: S(x) -> Q(x). Therefore P(a).