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