Translate the following inference to logic notation: For all x, if x_7 were a nurse, then x_7 is a lawyer. For all x, x_7 is a scientist if and only if x_7 is a lawyer. There is at least one x for which x_7 is a nurse. Therefore there is at least one x for which x_7 is a scientist.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). exists x: P(x). Therefore exists x: R(x).