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