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