Translate the following inference to logic notation: For all x, if x_6 were an electrician, then x_6 is a sailor. For all x, if x_6 works, then x_6 is an electrician. There is at least one x for which x_6 will work if and only if x_6 is a sailor. Therefore there is at least one x for which x_6 is a sailor if and only if x_6 will work.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: R(x) <-> Q(x). Therefore exists x: Q(x) <-> R(x).