Translate the following inference to logic notation: For all x, x_7 is a police officer. There is at least one x for which if x_7 plays squash, then x_7 is sad. For all x, x_7 is a nurse if and only if x_7 is sad. For all x, x_7 is not a police officer or x_7 is a nurse. Therefore there is at least one x for which x_7 is sad.
forall x: P(x). exists x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: ~P(x) or S(x). Therefore exists x: R(x).