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