Translate the following inference to logic notation: For all x, if x_7 writes a letter, then x_7 is playing squash. For all x, if x_7 works, then x_7 is running. For all x, x_7 will work. There is at least one x for which x_7 will write a letter. Therefore there is at least one x for which x_7 will play squash and x_7 will go running.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: R(x). exists x: P(x). Therefore exists x: Q(x) and S(x).