Translate the following inference to logic notation: There is at least one x for which if y_1 were sad, then y_1 is an electrician. For all x, y_1 is sad or y_1 is not an electrician. Therefore there is at least one x for which y_1 is an electrician if and only if y_1 is sad.
exists x: P(x) -> Q(x). forall x: P(x) or ~Q(x). Therefore exists x: Q(x) <-> P(x).