Translate the following inference to logic notation: There is at least one x for which if x_6 were excited, then x_6 is happy. For all x, if x_6 were poor, then x_6 is excited. For all x, if x_6 were happy, then x_6 is excited. For all x, x_6 is poor or x_6 is happy. Therefore there is at least one x for which x_6 is excited.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> P(x). forall x: R(x) or Q(x). Therefore exists x: P(x).