Translate the following inference to logic notation: For all x, x_10 will sleep. For all x, if x_10 takes a plane, then x_10 is cooking. There is at least one x for which if x_10 listens to a song, then x_10 is cooking. For all x, x_10 will take a plane if and only if x_10 will sleep. Therefore there is at least one x for which x_10 will cook.
forall x: P(x). forall x: Q(x) -> R(x). exists x: S(x) -> R(x). forall x: Q(x) <-> P(x). Therefore exists x: R(x).