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