Translate the following inference to logic notation: For all x, y is an electrician or y is sad. For all x, if y were sad, then y is writing a letter. For all x, y is not an electrician. There is at least one x for which if y writes a letter, then y is a carpenter. Therefore there is at least one x for which y is a carpenter.
forall x: P(x) or Q(x). forall x: Q(x) -> R(x). forall x: ~P(x). exists x: R(x) -> S(x). Therefore exists x: S(x).