Translate the following inference to logic notation: For all x, x_11 will cook or x_11 is not a scientist. For all x, x_11 is a scientist if and only if x_11 will cook. Therefore if Elisabeth were a scientist, then Elisabeth is cooking.
forall x: P(x) or ~Q(x). forall x: Q(x) <-> P(x). Therefore Q(a) -> P(a).