Translate the following inference to logic notation: For all x, x_7 is a sailor if and only if x_7 is a nurse. For all x, x_7 is a sailor or x_7 will sleep. There is at least one x for which x_7 is a mechanic. For all x, if x_7 sleeps, then x_7 is a nurse. Therefore there is at least one x for which x_7 is a mechanic and x_7 is a nurse.
forall x: P(x) <-> Q(x). forall x: P(x) or R(x). exists x: S(x). forall x: R(x) -> Q(x). Therefore exists x: S(x) and Q(x).