Translate the following inference to logic notation: There is at least one x for which x_7 will listen to a song if and only if x_7 will write a letter. For all x, if x_7 writes a letter, then x_7 is running. For all x, x_7 will take a plane if and only if x_7 will go running. For all x, x_7 will not take a plane. Therefore there is at least one x for which x_7 will not listen to a song.
exists x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: ~S(x). Therefore exists x: ~P(x).