Translate the following inference to logic notation: For all x, if x_10 writes a letter, then x_10 is taking a plane. For all x, x_10 will listen to a song or x_10 will play squash. There is at least one x for which x_10 will not take a plane. For all x, x_10 will write a letter if and only if x_10 will listen to a song. Therefore there is at least one x for which x_10 will play squash.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). exists x: ~Q(x). forall x: P(x) <-> R(x). Therefore exists x: S(x).