Translate the following inference to logic notation: For all x, if z were bored, then z is sad. There is at least one x for which z will cook or z is not bored. For all x, if z were sad, then z is bored. Therefore there is at least one x for which if z were sad, then z is cooking.
forall x: P(x) -> Q(x). exists x: R(x) or ~P(x). forall x: Q(x) -> P(x). Therefore exists x: Q(x) -> R(x).