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