Translate the following inference to logic notation: For all x, if x_7 plays tennis, then x_7 is writing a letter. For all x, x_7 will sleep. There is at least one x for which if x_7 were a poet, then x_7 is writing a letter. For all x, x_7 is a poet or x_7 will play tennis. Therefore there is at least one x for which x_7 will sleep and x_7 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x). exists x: S(x) -> Q(x). forall x: S(x) or P(x). Therefore exists x: R(x) and Q(x).