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